{- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 1998 \section[TyCoRep]{Type and Coercion - friends' interface} Note [The Type-related module hierarchy] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Class CoAxiom TyCon imports Class, CoAxiom TyCoRep imports Class, CoAxiom, TyCon TysPrim imports TyCoRep ( including mkTyConTy ) Kind imports TysPrim ( mainly for primitive kinds ) Type imports Kind Coercion imports Type -} -- We expose the relevant stuff from this module via the Type module {-# OPTIONS_HADDOCK hide #-} {-# LANGUAGE CPP, DeriveDataTypeable, DeriveFunctor, DeriveFoldable, DeriveTraversable, MultiWayIf #-} {-# LANGUAGE ImplicitParams #-} module TyCoRep ( TyThing(..), Type(..), TyBinder(..), TyLit(..), KindOrType, Kind, PredType, ThetaType, -- Synonyms VisibilityFlag(..), -- Coercions Coercion(..), LeftOrRight(..), UnivCoProvenance(..), CoercionHole(..), CoercionN, CoercionR, CoercionP, KindCoercion, -- Functions over types mkTyConTy, mkTyVarTy, mkTyVarTys, mkFunTy, mkFunTys, mkForAllTys, isLiftedTypeKind, isUnliftedTypeKind, isCoercionType, isRuntimeRepTy, isRuntimeRepVar, isRuntimeRepKindedTy, dropRuntimeRepArgs, sameVis, -- Functions over binders binderType, delBinderVar, isInvisibleBinder, isVisibleBinder, isNamedBinder, isAnonBinder, -- Functions over coercions pickLR, -- Pretty-printing pprType, pprParendType, pprTypeApp, pprTvBndr, pprTvBndrs, pprTyThing, pprTyThingCategory, pprSigmaType, pprTheta, pprForAll, pprForAllImplicit, pprUserForAll, pprThetaArrowTy, pprClassPred, pprKind, pprParendKind, pprTyLit, TyPrec(..), maybeParen, pprTcAppCo, pprTcAppTy, pprPrefixApp, pprArrowChain, ppr_type, pprDataCons, -- * Free variables tyCoVarsOfType, tyCoVarsOfTypeDSet, tyCoVarsOfTypes, tyCoVarsOfTypesDSet, tyCoVarsBndrAcc, tyCoVarsOfTypeAcc, tyCoVarsOfTypeList, tyCoVarsOfTypesAcc, tyCoVarsOfTypesList, closeOverKindsDSet, closeOverKindsAcc, coVarsOfType, coVarsOfTypes, coVarsOfCo, coVarsOfCos, tyCoVarsOfCo, tyCoVarsOfCos, tyCoVarsOfCoDSet, tyCoVarsOfCoAcc, tyCoVarsOfCosAcc, tyCoVarsOfCoList, tyCoVarsOfProv, closeOverKinds, tyCoVarsOfTelescope, -- * Substitutions TCvSubst(..), TvSubstEnv, CvSubstEnv, emptyTvSubstEnv, emptyCvSubstEnv, composeTCvSubstEnv, composeTCvSubst, emptyTCvSubst, mkEmptyTCvSubst, isEmptyTCvSubst, mkTCvSubst, mkTvSubst, getTvSubstEnv, getCvSubstEnv, getTCvInScope, isInScope, notElemTCvSubst, setTvSubstEnv, setCvSubstEnv, zapTCvSubst, extendTCvInScope, extendTCvInScopeList, extendTCvInScopeSet, extendTCvSubst, extendCvSubst, extendCvSubstWithClone, extendTvSubst, extendTvSubstWithClone, extendTvSubstList, extendTvSubstAndInScope, extendTvSubstBinder, unionTCvSubst, zipTyEnv, zipCoEnv, mkTyCoInScopeSet, zipTvSubst, zipCvSubst, zipTyBinderSubst, mkTvSubstPrs, substTyWith, substTyWithCoVars, substTysWith, substTysWithCoVars, substCoWith, substTy, substTyAddInScope, substTyUnchecked, substTysUnchecked, substThetaUnchecked, substTyWithBindersUnchecked, substTyWithUnchecked, substCoUnchecked, substCoWithUnchecked, substTyWithBinders, substTyWithInScope, substTys, substTheta, lookupTyVar, substTyVarBndr, substCo, substCos, substCoVar, substCoVars, lookupCoVar, substCoVarBndr, cloneTyVarBndr, cloneTyVarBndrs, substTyVar, substTyVars, substForAllCoBndr, substTyVarBndrCallback, substForAllCoBndrCallback, substCoVarBndrCallback, -- * Tidying type related things up for printing tidyType, tidyTypes, tidyOpenType, tidyOpenTypes, tidyOpenKind, tidyTyCoVarBndr, tidyTyCoVarBndrs, tidyFreeTyCoVars, tidyOpenTyCoVar, tidyOpenTyCoVars, tidyTyVarOcc, tidyTopType, tidyKind, tidyCo, tidyCos, tidyTyBinder, tidyTyBinders ) where #include "HsVersions.h" import {-# SOURCE #-} DataCon( dataConTyCon, dataConFullSig , dataConUnivTyBinders, dataConExTyBinders , DataCon, filterEqSpec ) import {-# SOURCE #-} Type( isPredTy, isCoercionTy, mkAppTy , tyCoVarsOfTypesWellScoped, varSetElemsWellScoped , partitionInvisibles, coreView, typeKind , eqType ) -- Transitively pulls in a LOT of stuff, better to break the loop import {-# SOURCE #-} Coercion import {-# SOURCE #-} ConLike ( ConLike(..) ) import {-# SOURCE #-} TysWiredIn ( ptrRepLiftedTy ) -- friends: import Var import VarEnv import VarSet import Name hiding ( varName ) import BasicTypes import TyCon import Class import CoAxiom import FV -- others import PrelNames import Binary import Outputable import DynFlags import StaticFlags ( opt_PprStyle_Debug ) import FastString import Pair import UniqSupply import Util import UniqFM -- libraries import qualified Data.Data as Data hiding ( TyCon ) import Data.List import Data.IORef ( IORef ) -- for CoercionHole #if __GLASGOW_HASKELL__ > 710 import GHC.Stack (CallStack) #endif {- %************************************************************************ %* * \subsection{The data type} %* * %************************************************************************ -} -- | The key representation of types within the compiler -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in coreSyn/CoreLint.hs data Type -- See Note [Non-trivial definitional equality] = TyVarTy Var -- ^ Vanilla type or kind variable (*never* a coercion variable) | AppTy -- See Note [AppTy rep] Type Type -- ^ Type application to something other than a 'TyCon'. Parameters: -- -- 1) Function: must /not/ be a 'TyConApp', -- must be another 'AppTy', or 'TyVarTy' -- -- 2) Argument type | TyConApp -- See Note [AppTy rep] TyCon [KindOrType] -- ^ Application of a 'TyCon', including newtypes /and/ synonyms. -- Invariant: saturated applications of 'FunTyCon' must -- use 'FunTy' and saturated synonyms must use their own -- constructors. However, /unsaturated/ 'FunTyCon's -- do appear as 'TyConApp's. -- Parameters: -- -- 1) Type constructor being applied to. -- -- 2) Type arguments. Might not have enough type arguments -- here to saturate the constructor. -- Even type synonyms are not necessarily saturated; -- for example unsaturated type synonyms -- can appear as the right hand side of a type synonym. | ForAllTy TyBinder Type -- ^ A Π type. -- This includes arrow types, constructed with -- @ForAllTy (Anon ...)@. See also Note [TyBinder]. | LitTy TyLit -- ^ Type literals are similar to type constructors. | CastTy Type KindCoercion -- ^ A kind cast. The coercion is always nominal. -- INVARIANT: The cast is never refl. -- INVARIANT: The cast is "pushed down" as far as it -- can go. See Note [Pushing down casts] | CoercionTy Coercion -- ^ Injection of a Coercion into a type -- This should only ever be used in the RHS of an AppTy, -- in the list of a TyConApp, when applying a promoted -- GADT data constructor deriving (Data.Data, Data.Typeable) -- NOTE: Other parts of the code assume that type literals do not contain -- types or type variables. data TyLit = NumTyLit Integer | StrTyLit FastString deriving (Eq, Ord, Data.Data, Data.Typeable) -- | A 'TyBinder' represents an argument to a function. TyBinders can be dependent -- ('Named') or nondependent ('Anon'). They may also be visible or not. -- See also Note [TyBinder] data TyBinder = Named TyVar VisibilityFlag -- Always a TyVar (not CoVar or Id) | Anon Type -- Visibility is determined by the type (Constraint vs. *) deriving (Data.Typeable, Data.Data) -- | Is something required to appear in source Haskell ('Visible'), -- permitted by request ('Specified') (visible type application), or -- prohibited entirely from appearing in source Haskell ('Invisible')? -- Examples in Note [VisibilityFlag] data VisibilityFlag = Visible | Specified | Invisible deriving (Eq, Data.Typeable, Data.Data) -- | Do these denote the same level of visibility? Except that -- 'Specified' and 'Invisible' are considered the same. Used -- for printing. sameVis :: VisibilityFlag -> VisibilityFlag -> Bool sameVis Visible Visible = True sameVis Visible _ = False sameVis _ Visible = False sameVis _ _ = True instance Binary VisibilityFlag where put_ bh Visible = putByte bh 0 put_ bh Specified = putByte bh 1 put_ bh Invisible = putByte bh 2 get bh = do h <- getByte bh case h of 0 -> return Visible 1 -> return Specified _ -> return Invisible type KindOrType = Type -- See Note [Arguments to type constructors] -- | The key type representing kinds in the compiler. type Kind = Type {- Note [TyBinder] ~~~~~~~~~~~~~~~ This represents the type of binders -- that is, the type of an argument to a Pi-type. GHC Core currently supports two different Pi-types: a non-dependent function, written with ->, and a dependent compile-time-only polytype, written with forall. Both Pi-types classify terms/types that take an argument. In other words, if `x` is either a function or a polytype, `x arg` makes sense (for an appropriate `arg`). It is thus often convenient to group Pi-types together. This is ForAllTy. The two constructors for TyBinder sort out the two different possibilities. `Named` builds a polytype, while `Anon` builds an ordinary function. (ForAllTy (Anon arg) res used to be called FunTy arg res.) Note [The kind invariant] ~~~~~~~~~~~~~~~~~~~~~~~~~ The kinds # UnliftedTypeKind OpenKind super-kind of *, # can never appear under an arrow or type constructor in a kind; they can only be at the top level of a kind. It follows that primitive TyCons, which have a naughty pseudo-kind State# :: * -> # must always be saturated, so that we can never get a type whose kind has a UnliftedTypeKind or ArgTypeKind underneath an arrow. Nor can we abstract over a type variable with any of these kinds. k :: = kk | # | ArgKind | (#) | OpenKind kk :: = * | kk -> kk | T kk1 ... kkn So a type variable can only be abstracted kk. Note [Arguments to type constructors] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Because of kind polymorphism, in addition to type application we now have kind instantiation. We reuse the same notations to do so. For example: Just (* -> *) Maybe Right * Nat Zero are represented by: TyConApp (PromotedDataCon Just) [* -> *, Maybe] TyConApp (PromotedDataCon Right) [*, Nat, (PromotedDataCon Zero)] Important note: Nat is used as a *kind* and not as a type. This can be confusing, since type-level Nat and kind-level Nat are identical. We use the kind of (PromotedDataCon Right) to know if its arguments are kinds or types. This kind instantiation only happens in TyConApp currently. Note [Pushing down casts] ~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have (a :: k1 -> *), (b :: k1), and (co :: * ~ q). The type (a b |> co) is `eqType` to ((a |> co') b), where co' = (->) <k1> co. Thus, to make this visible to functions that inspect types, we always push down coercions, preferring the second form. Note that this also applies to TyConApps! Note [Non-trivial definitional equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Is Int |> <*> the same as Int? YES! In order to reduce headaches, we decide that any reflexive casts in types are just ignored. More generally, the `eqType` function, which defines Core's type equality relation, ignores casts and coercion arguments, as long as the two types have the same kind. This allows us to be a little sloppier in keeping track of coercions, which is a good thing. It also means that eqType does not depend on eqCoercion, which is also a good thing. Why is this sensible? That is, why is something different than α-equivalence appropriate for the implementation of eqType? Anything smaller than ~ and homogeneous is an appropriate definition for equality. The type safety of FC depends only on ~. Let's say η : τ ~ σ. Any expression of type τ can be transmuted to one of type σ at any point by casting. The same is true of types of type τ. So in some sense, τ and σ are interchangeable. But let's be more precise. If we examine the typing rules of FC (say, those in http://www.cis.upenn.edu/~eir/papers/2015/equalities/equalities-extended.pdf) there are several places where the same metavariable is used in two different premises to a rule. (For example, see Ty_App.) There is an implicit equality check here. What definition of equality should we use? By convention, we use α-equivalence. Take any rule with one (or more) of these implicit equality checks. Then there is an admissible rule that uses ~ instead of the implicit check, adding in casts as appropriate. The only problem here is that ~ is heterogeneous. To make the kinds work out in the admissible rule that uses ~, it is necessary to homogenize the coercions. That is, if we have η : (τ : κ1) ~ (σ : κ2), then we don't use η; we use η |> kind η, which is homogeneous. The effect of this all is that eqType, the implementation of the implicit equality check, can use any homogeneous relation that is smaller than ~, as those rules must also be admissible. What would go wrong if we insisted on the casts matching? See the beginning of Section 8 in the unpublished paper above. Theoretically, nothing at all goes wrong. But in practical terms, getting the coercions right proved to be nightmarish. And types would explode: during kind-checking, we often produce reflexive kind coercions. When we try to cast by these, mkCastTy just discards them. But if we used an eqType that distinguished between Int and Int |> <*>, then we couldn't discard -- the output of kind-checking would be enormous, and we would need enormous casts with lots of CoherenceCo's to straighten them out. Would anything go wrong if eqType respected type families? No, not at all. But that makes eqType rather hard to implement. Thus, the guideline for eqType is that it should be the largest easy-to-implement relation that is still smaller than ~ and homogeneous. The precise choice of relation is somewhat incidental, as long as the smart constructors and destructors in Type respect whatever relation is chosen. Another helpful principle with eqType is this: ** If (t1 eqType t2) then I can replace t1 by t2 anywhere. ** This principle also tells us that eqType must relate only types with the same kinds. Note [VisibilityFlag] ~~~~~~~~~~~~~~~~~~~~~ All named binders are equipped with a visibility flag, which says whether or not arguments for this binder should be visible (explicit) in source Haskell. Historically, all named binders (that is, polytype binders) have been Invisible. But now it's more complicated. Invisible: Argument does not ever appear in source Haskell. With visible type application, only GHC-generated polytypes have Invisible binders. This exactly corresponds to "generalized" variables from the Visible Type Applications paper (ESOP'16). Example: f x = x `f` will be inferred to have type `forall a. a -> a`, where `a` is Invisible. Note that there is no type annotation for `f`. Printing: With -fprint-explicit-foralls, Invisible binders are written in braces. Otherwise, they are printed like Specified binders. Specified: The argument for this binder may appear in source Haskell only with visible type application. Otherwise, it is omitted. Example: id :: forall a. a -> a `a` is a Specified binder, because you can say `id @Int` in source Haskell. Example: const :: a -> b -> a Both `a` and `b` are Specified binders, even though they are not bound by an explicit forall. Printing: a list of Specified binders are put between `forall` and `.`: const :: forall a b. a -> b -> a Visible: The argument must be given. Visible binders come up only with TypeInType. Example: data Proxy k (a :: k) = P The kind of Proxy is forall k -> k -> *, where k is a Visible binder. Printing: As in the example above, Visible binders are put between `forall` and `->`. This syntax is not parsed (yet), however. ------------------------------------- Note [PredTy] -} -- | A type of the form @p@ of kind @Constraint@ represents a value whose type is -- the Haskell predicate @p@, where a predicate is what occurs before -- the @=>@ in a Haskell type. -- -- We use 'PredType' as documentation to mark those types that we guarantee to have -- this kind. -- -- It can be expanded into its representation, but: -- -- * The type checker must treat it as opaque -- -- * The rest of the compiler treats it as transparent -- -- Consider these examples: -- -- > f :: (Eq a) => a -> Int -- > g :: (?x :: Int -> Int) => a -> Int -- > h :: (r\l) => {r} => {l::Int | r} -- -- Here the @Eq a@ and @?x :: Int -> Int@ and @r\l@ are all called \"predicates\" type PredType = Type -- | A collection of 'PredType's type ThetaType = [PredType] {- (We don't support TREX records yet, but the setup is designed to expand to allow them.) A Haskell qualified type, such as that for f,g,h above, is represented using * a FunTy for the double arrow * with a type of kind Constraint as the function argument The predicate really does turn into a real extra argument to the function. If the argument has type (p :: Constraint) then the predicate p is represented by evidence of type p. %************************************************************************ %* * Simple constructors %* * %************************************************************************ These functions are here so that they can be used by TysPrim, which in turn is imported by Type -} -- named with "Only" to prevent naive use of mkTyVarTy mkTyVarTy :: TyVar -> Type mkTyVarTy v = ASSERT2( isTyVar v, ppr v <+> dcolon <+> ppr (tyVarKind v) ) TyVarTy v mkTyVarTys :: [TyVar] -> [Type] mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy infixr 3 `mkFunTy` -- Associates to the right -- | Make an arrow type mkFunTy :: Type -> Type -> Type mkFunTy arg res = ForAllTy (Anon arg) res -- | Make nested arrow types mkFunTys :: [Type] -> Type -> Type mkFunTys tys ty = foldr mkFunTy ty tys -- | Wraps foralls over the type using the provided 'TyVar's from left to right mkForAllTys :: [TyBinder] -> Type -> Type mkForAllTys tyvars ty = foldr ForAllTy ty tyvars -- | Does this type classify a core (unlifted) Coercion? -- At either role nominal or reprsentational -- (t1 ~# t2) or (t1 ~R# t2) isCoercionType :: Type -> Bool isCoercionType (TyConApp tc tys) | (tc `hasKey` eqPrimTyConKey) || (tc `hasKey` eqReprPrimTyConKey) , length tys == 4 = True isCoercionType _ = False binderType :: TyBinder -> Type binderType (Named v _) = varType v binderType (Anon ty) = ty -- | Remove the binder's variable from the set, if the binder has -- a variable. delBinderVar :: VarSet -> TyBinder -> VarSet delBinderVar vars (Named tv _) = vars `delVarSet` tv delBinderVar vars (Anon {}) = vars -- | Remove the binder's variable from the set, if the binder has -- a variable. delBinderVarFV :: TyBinder -> FV -> FV delBinderVarFV (Named tv _) vars fv_cand in_scope acc = delFV tv vars fv_cand in_scope acc delBinderVarFV (Anon {}) vars fv_cand in_scope acc = vars fv_cand in_scope acc -- | Does this binder bind an invisible argument? isInvisibleBinder :: TyBinder -> Bool isInvisibleBinder (Named _ vis) = vis /= Visible isInvisibleBinder (Anon ty) = isPredTy ty -- | Does this binder bind a visible argument? isVisibleBinder :: TyBinder -> Bool isVisibleBinder = not . isInvisibleBinder isNamedBinder :: TyBinder -> Bool isNamedBinder (Named {}) = True isNamedBinder _ = False isAnonBinder :: TyBinder -> Bool isAnonBinder (Anon {}) = True isAnonBinder _ = False -- | Create the plain type constructor type which has been applied to no type arguments at all. mkTyConTy :: TyCon -> Type mkTyConTy tycon = TyConApp tycon [] {- Some basic functions, put here to break loops eg with the pretty printer -} -- | This version considers Constraint to be distinct from *. isLiftedTypeKind :: Kind -> Bool isLiftedTypeKind ki | Just ki' <- coreView ki = isLiftedTypeKind ki' isLiftedTypeKind (TyConApp tc [TyConApp ptr_rep []]) = tc `hasKey` tYPETyConKey && ptr_rep `hasKey` ptrRepLiftedDataConKey isLiftedTypeKind _ = False isUnliftedTypeKind :: Kind -> Bool isUnliftedTypeKind ki | Just ki' <- coreView ki = isUnliftedTypeKind ki' isUnliftedTypeKind (TyConApp tc [TyConApp ptr_rep []]) | tc `hasKey` tYPETyConKey , ptr_rep `hasKey` ptrRepLiftedDataConKey = False isUnliftedTypeKind (TyConApp tc [arg]) = tc `hasKey` tYPETyConKey && isEmptyVarSet (tyCoVarsOfType arg) -- all other possibilities are unlifted isUnliftedTypeKind _ = False -- | Is this the type 'RuntimeRep'? isRuntimeRepTy :: Type -> Bool isRuntimeRepTy ty | Just ty' <- coreView ty = isRuntimeRepTy ty' isRuntimeRepTy (TyConApp tc []) = tc `hasKey` runtimeRepTyConKey isRuntimeRepTy _ = False -- | Is this a type of kind RuntimeRep? (e.g. PtrRep) isRuntimeRepKindedTy :: Type -> Bool isRuntimeRepKindedTy = isRuntimeRepTy . typeKind -- | Is a tyvar of type 'RuntimeRep'? isRuntimeRepVar :: TyVar -> Bool isRuntimeRepVar = isRuntimeRepTy . tyVarKind -- | Drops prefix of RuntimeRep constructors in 'TyConApp's. Useful for e.g. -- dropping 'PtrRep arguments of unboxed tuple TyCon applications: -- -- dropRuntimeRepArgs [ 'PtrRepLifted, 'PtrRepUnlifted -- , String, Int# ] == [String, Int#] -- dropRuntimeRepArgs :: [Type] -> [Type] dropRuntimeRepArgs = dropWhile isRuntimeRepKindedTy {- %************************************************************************ %* * Coercions %* * %************************************************************************ -} -- | A 'Coercion' is concrete evidence of the equality/convertibility -- of two types. -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in coreSyn/CoreLint.hs data Coercion -- Each constructor has a "role signature", indicating the way roles are -- propagated through coercions. -- - P, N, and R stand for coercions of the given role -- - e stands for a coercion of a specific unknown role -- (think "role polymorphism") -- - "e" stands for an explicit role parameter indicating role e. -- - _ stands for a parameter that is not a Role or Coercion. -- These ones mirror the shape of types = -- Refl :: "e" -> _ -> e Refl Role Type -- See Note [Refl invariant] -- Invariant: applications of (Refl T) to a bunch of identity coercions -- always show up as Refl. -- For example (Refl T) (Refl a) (Refl b) shows up as (Refl (T a b)). -- Applications of (Refl T) to some coercions, at least one of -- which is NOT the identity, show up as TyConAppCo. -- (They may not be fully saturated however.) -- ConAppCo coercions (like all coercions other than Refl) -- are NEVER the identity. -- Use (Refl Representational _), not (SubCo (Refl Nominal _)) -- These ones simply lift the correspondingly-named -- Type constructors into Coercions -- TyConAppCo :: "e" -> _ -> ?? -> e -- See Note [TyConAppCo roles] | TyConAppCo Role TyCon [Coercion] -- lift TyConApp -- The TyCon is never a synonym; -- we expand synonyms eagerly -- But it can be a type function | AppCo Coercion CoercionN -- lift AppTy -- AppCo :: e -> N -> e -- See Note [Forall coercions] | ForAllCo TyVar KindCoercion Coercion -- ForAllCo :: _ -> N -> e -> e -- These are special | CoVarCo CoVar -- :: _ -> (N or R) -- result role depends on the tycon of the variable's type -- AxiomInstCo :: e -> _ -> [N] -> e | AxiomInstCo (CoAxiom Branched) BranchIndex [Coercion] -- See also [CoAxiom index] -- The coercion arguments always *precisely* saturate -- arity of (that branch of) the CoAxiom. If there are -- any left over, we use AppCo. -- See [Coercion axioms applied to coercions] | UnivCo UnivCoProvenance Role Type Type -- :: _ -> "e" -> _ -> _ -> e | SymCo Coercion -- :: e -> e | TransCo Coercion Coercion -- :: e -> e -> e -- The number coercions should match exactly the expectations -- of the CoAxiomRule (i.e., the rule is fully saturated). | AxiomRuleCo CoAxiomRule [Coercion] | NthCo Int Coercion -- Zero-indexed; decomposes (T t0 ... tn) -- :: _ -> e -> ?? (inverse of TyConAppCo, see Note [TyConAppCo roles]) -- Using NthCo on a ForAllCo gives an N coercion always -- See Note [NthCo and newtypes] | LRCo LeftOrRight CoercionN -- Decomposes (t_left t_right) -- :: _ -> N -> N | InstCo Coercion CoercionN -- :: e -> N -> e -- See Note [InstCo roles] -- Coherence applies a coercion to the left-hand type of another coercion -- See Note [Coherence] | CoherenceCo Coercion KindCoercion -- :: e -> N -> e -- Extract a kind coercion from a (heterogeneous) type coercion -- NB: all kind coercions are Nominal | KindCo Coercion -- :: e -> N | SubCo CoercionN -- Turns a ~N into a ~R -- :: N -> R deriving (Data.Data, Data.Typeable) type CoercionN = Coercion -- always nominal type CoercionR = Coercion -- always representational type CoercionP = Coercion -- always phantom type KindCoercion = CoercionN -- always nominal -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in coreSyn/CoreLint.hs data LeftOrRight = CLeft | CRight deriving( Eq, Data.Data, Data.Typeable ) instance Binary LeftOrRight where put_ bh CLeft = putByte bh 0 put_ bh CRight = putByte bh 1 get bh = do { h <- getByte bh ; case h of 0 -> return CLeft _ -> return CRight } pickLR :: LeftOrRight -> (a,a) -> a pickLR CLeft (l,_) = l pickLR CRight (_,r) = r {- Note [Refl invariant] ~~~~~~~~~~~~~~~~~~~~~ Invariant 1: Coercions have the following invariant Refl is always lifted as far as possible. You might think that a consequencs is: Every identity coercions has Refl at the root But that's not quite true because of coercion variables. Consider g where g :: Int~Int Left h where h :: Maybe Int ~ Maybe Int etc. So the consequence is only true of coercions that have no coercion variables. Note [Coercion axioms applied to coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The reason coercion axioms can be applied to coercions and not just types is to allow for better optimization. There are some cases where we need to be able to "push transitivity inside" an axiom in order to expose further opportunities for optimization. For example, suppose we have C a : t[a] ~ F a g : b ~ c and we want to optimize sym (C b) ; t[g] ; C c which has the kind F b ~ F c (stopping through t[b] and t[c] along the way). We'd like to optimize this to just F g -- but how? The key is that we need to allow axioms to be instantiated by *coercions*, not just by types. Then we can (in certain cases) push transitivity inside the axiom instantiations, and then react opposite-polarity instantiations of the same axiom. In this case, e.g., we match t[g] against the LHS of (C c)'s kind, to obtain the substitution a |-> g (note this operation is sort of the dual of lifting!) and hence end up with C g : t[b] ~ F c which indeed has the same kind as t[g] ; C c. Now we have sym (C b) ; C g which can be optimized to F g. Note [CoAxiom index] ~~~~~~~~~~~~~~~~~~~~ A CoAxiom has 1 or more branches. Each branch has contains a list of the free type variables in that branch, the LHS type patterns, and the RHS type for that branch. When we apply an axiom to a list of coercions, we must choose which branch of the axiom we wish to use, as the different branches may have different numbers of free type variables. (The number of type patterns is always the same among branches, but that doesn't quite concern us here.) The Int in the AxiomInstCo constructor is the 0-indexed number of the chosen branch. Note [Forall coercions] ~~~~~~~~~~~~~~~~~~~~~~~ Constructing coercions between forall-types can be a bit tricky, because the kinds of the bound tyvars can be different. The typing rule is: kind_co : k1 ~ k2 tv1:k1 |- co : t1 ~ t2 ------------------------------------------------------------------- ForAllCo tv1 kind_co co : all tv1:k1. t1 ~ all tv1:k2. (t2[tv1 |-> tv1 |> sym kind_co]) First, the TyVar stored in a ForAllCo is really an optimisation: this field should be a Name, as its kind is redundant. Thinking of the field as a Name is helpful in understanding what a ForAllCo means. The idea is that kind_co gives the two kinds of the tyvar. See how, in the conclusion, tv1 is assigned kind k1 on the left but kind k2 on the right. Of course, a type variable can't have different kinds at the same time. So, we arbitrarily prefer the first kind when using tv1 in the inner coercion co, which shows that t1 equals t2. The last wrinkle is that we need to fix the kinds in the conclusion. In t2, tv1 is assumed to have kind k1, but it has kind k2 in the conclusion of the rule. So we do a kind-fixing substitution, replacing (tv1:k1) with (tv1:k2) |> sym kind_co. This substitution is slightly bizarre, because it mentions the same name with different kinds, but it *is* well-kinded, noting that `(tv1:k2) |> sym kind_co` has kind k1. This all really would work storing just a Name in the ForAllCo. But we can't add Names to, e.g., VarSets, and there generally is just an impedence mismatch in a bunch of places. So we use tv1. When we need tv2, we can use setTyVarKind. Note [Coherence] ~~~~~~~~~~~~~~~~ The Coherence typing rule is thus: g1 : s ~ t s : k1 g2 : k1 ~ k2 ------------------------------------ CoherenceCo g1 g2 : (s |> g2) ~ t While this looks (and is) unsymmetric, a combination of other coercion combinators can make the symmetric version. For role information, see Note [Roles and kind coercions]. Note [Predicate coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have g :: a~b How can we coerce between types ([c]~a) => [a] -> c and ([c]~b) => [b] -> c where the equality predicate *itself* differs? Answer: we simply treat (~) as an ordinary type constructor, so these types really look like ((~) [c] a) -> [a] -> c ((~) [c] b) -> [b] -> c So the coercion between the two is obviously ((~) [c] g) -> [g] -> c Another way to see this to say that we simply collapse predicates to their representation type (see Type.coreView and Type.predTypeRep). This collapse is done by mkPredCo; there is no PredCo constructor in Coercion. This is important because we need Nth to work on predicates too: Nth 1 ((~) [c] g) = g See Simplify.simplCoercionF, which generates such selections. Note [Roles] ~~~~~~~~~~~~ Roles are a solution to the GeneralizedNewtypeDeriving problem, articulated in Trac #1496. The full story is in docs/core-spec/core-spec.pdf. Also, see http://ghc.haskell.org/trac/ghc/wiki/RolesImplementation Here is one way to phrase the problem: Given: newtype Age = MkAge Int type family F x type instance F Age = Bool type instance F Int = Char This compiles down to: axAge :: Age ~ Int axF1 :: F Age ~ Bool axF2 :: F Int ~ Char Then, we can make: (sym (axF1) ; F axAge ; axF2) :: Bool ~ Char Yikes! The solution is _roles_, as articulated in "Generative Type Abstraction and Type-level Computation" (POPL 2010), available at http://www.seas.upenn.edu/~sweirich/papers/popl163af-weirich.pdf The specification for roles has evolved somewhat since that paper. For the current full details, see the documentation in docs/core-spec. Here are some highlights. We label every equality with a notion of type equivalence, of which there are three options: Nominal, Representational, and Phantom. A ground type is nominally equivalent only with itself. A newtype (which is considered a ground type in Haskell) is representationally equivalent to its representation. Anything is "phantomly" equivalent to anything else. We use "N", "R", and "P" to denote the equivalences. The axioms above would be: axAge :: Age ~R Int axF1 :: F Age ~N Bool axF2 :: F Age ~N Char Then, because transitivity applies only to coercions proving the same notion of equivalence, the above construction is impossible. However, there is still an escape hatch: we know that any two types that are nominally equivalent are representationally equivalent as well. This is what the form SubCo proves -- it "demotes" a nominal equivalence into a representational equivalence. So, it would seem the following is possible: sub (sym axF1) ; F axAge ; sub axF2 :: Bool ~R Char -- WRONG What saves us here is that the arguments to a type function F, lifted into a coercion, *must* prove nominal equivalence. So, (F axAge) is ill-formed, and we are safe. Roles are attached to parameters to TyCons. When lifting a TyCon into a coercion (through TyConAppCo), we need to ensure that the arguments to the TyCon respect their roles. For example: data T a b = MkT a (F b) If we know that a1 ~R a2, then we know (T a1 b) ~R (T a2 b). But, if we know that b1 ~R b2, we know nothing about (T a b1) and (T a b2)! This is because the type function F branches on b's *name*, not representation. So, we say that 'a' has role Representational and 'b' has role Nominal. The third role, Phantom, is for parameters not used in the type's definition. Given the following definition data Q a = MkQ Int the Phantom role allows us to say that (Q Bool) ~R (Q Char), because we can construct the coercion Bool ~P Char (using UnivCo). See the paper cited above for more examples and information. Note [TyConAppCo roles] ~~~~~~~~~~~~~~~~~~~~~~~ The TyConAppCo constructor has a role parameter, indicating the role at which the coercion proves equality. The choice of this parameter affects the required roles of the arguments of the TyConAppCo. To help explain it, assume the following definition: type instance F Int = Bool -- Axiom axF : F Int ~N Bool newtype Age = MkAge Int -- Axiom axAge : Age ~R Int data Foo a = MkFoo a -- Role on Foo's parameter is Representational TyConAppCo Nominal Foo axF : Foo (F Int) ~N Foo Bool For (TyConAppCo Nominal) all arguments must have role Nominal. Why? So that Foo Age ~N Foo Int does *not* hold. TyConAppCo Representational Foo (SubCo axF) : Foo (F Int) ~R Foo Bool TyConAppCo Representational Foo axAge : Foo Age ~R Foo Int For (TyConAppCo Representational), all arguments must have the roles corresponding to the result of tyConRoles on the TyCon. This is the whole point of having roles on the TyCon to begin with. So, we can have Foo Age ~R Foo Int, if Foo's parameter has role R. If a Representational TyConAppCo is over-saturated (which is otherwise fine), the spill-over arguments must all be at Nominal. This corresponds to the behavior for AppCo. TyConAppCo Phantom Foo (UnivCo Phantom Int Bool) : Foo Int ~P Foo Bool All arguments must have role Phantom. This one isn't strictly necessary for soundness, but this choice removes ambiguity. The rules here dictate the roles of the parameters to mkTyConAppCo (should be checked by Lint). Note [NthCo and newtypes] ~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have newtype N a = MkN Int type role N representational This yields axiom NTCo:N :: forall a. N a ~R Int We can then build co :: forall a b. N a ~R N b co = NTCo:N a ; sym (NTCo:N b) for any `a` and `b`. Because of the role annotation on N, if we use NthCo, we'll get out a representational coercion. That is: NthCo 0 co :: forall a b. a ~R b Yikes! Clearly, this is terrible. The solution is simple: forbid NthCo to be used on newtypes if the internal coercion is representational. This is not just some corner case discovered by a segfault somewhere; it was discovered in the proof of soundness of roles and described in the "Safe Coercions" paper (ICFP '14). Note [InstCo roles] ~~~~~~~~~~~~~~~~~~~ Here is (essentially) the typing rule for InstCo: g :: (forall a. t1) ~r (forall a. t2) w :: s1 ~N s2 ------------------------------- InstCo InstCo g w :: (t1 [a |-> s1]) ~r (t2 [a |-> s2]) Note that the Coercion w *must* be nominal. This is necessary because the variable a might be used in a "nominal position" (that is, a place where role inference would require a nominal role) in t1 or t2. If we allowed w to be representational, we could get bogus equalities. A more nuanced treatment might be able to relax this condition somewhat, by checking if t1 and/or t2 use their bound variables in nominal ways. If not, having w be representational is OK. %************************************************************************ %* * UnivCoProvenance %* * %************************************************************************ A UnivCo is a coercion whose proof does not directly express its role and kind (indeed for some UnivCos, like UnsafeCoerceProv, there /is/ no proof). The different kinds of UnivCo are described by UnivCoProvenance. Really each is entirely separate, but they all share the need to represent their role and kind, which is done in the UnivCo constructor. -} -- | For simplicity, we have just one UnivCo that represents a coercion from -- some type to some other type, with (in general) no restrictions on the -- type. The UnivCoProvenance specifies more exactly what the coercion really -- is and why a program should (or shouldn't!) trust the coercion. -- It is reasonable to consider each constructor of 'UnivCoProvenance' -- as a totally independent coercion form; their only commonality is -- that they don't tell you what types they coercion between. (That info -- is in the 'UnivCo' constructor of 'Coercion'. data UnivCoProvenance = UnsafeCoerceProv -- ^ From @unsafeCoerce#@. These are unsound. | PhantomProv KindCoercion -- ^ See Note [Phantom coercions]. Only in Phantom -- roled coercions | ProofIrrelProv KindCoercion -- ^ From the fact that any two coercions are -- considered equivalent. See Note [ProofIrrelProv]. -- Can be used in Nominal or Representational coercions | PluginProv String -- ^ From a plugin, which asserts that this coercion -- is sound. The string is for the use of the plugin. | HoleProv CoercionHole -- ^ See Note [Coercion holes] deriving (Data.Data, Data.Typeable) instance Outputable UnivCoProvenance where ppr UnsafeCoerceProv = text "(unsafeCoerce#)" ppr (PhantomProv _) = text "(phantom)" ppr (ProofIrrelProv _) = text "(proof irrel.)" ppr (PluginProv str) = parens (text "plugin" <+> brackets (text str)) ppr (HoleProv hole) = parens (text "hole" <> ppr hole) -- | A coercion to be filled in by the type-checker. See Note [Coercion holes] data CoercionHole = CoercionHole { chUnique :: Unique -- ^ used only for debugging , chCoercion :: IORef (Maybe Coercion) } deriving (Data.Typeable) instance Data.Data CoercionHole where -- don't traverse? toConstr _ = abstractConstr "CoercionHole" gunfold _ _ = error "gunfold" dataTypeOf _ = mkNoRepType "CoercionHole" instance Outputable CoercionHole where ppr (CoercionHole u _) = braces (ppr u) {- Note [Phantom coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider data T a = T1 | T2 Then we have T s ~R T t for any old s,t. The witness for this is (TyConAppCo T Rep co), where (co :: s ~P t) is a phantom coercion built with PhantomProv. The role of the UnivCo is always Phantom. The Coercion stored is the (nominal) kind coercion between the types kind(s) ~N kind (t) Note [Coercion holes] ~~~~~~~~~~~~~~~~~~~~~~~~ During typechecking, constraint solving for type classes works by - Generate an evidence Id, d7 :: Num a - Wrap it in a Wanted constraint, [W] d7 :: Num a - Use the evidence Id where the evidence is needed - Solve the constraint later - When solved, add an enclosing let-binding let d7 = .... in .... which actually binds d7 to the (Num a) evidence For equality constraints we use a different strategy. See Note [The equality types story] in TysPrim for background on equality constraints. - For boxed equality constraints, (t1 ~N t2) and (t1 ~R t2), it's just like type classes above. (Indeed, boxed equality constraints *are* classes.) - But for /unboxed/ equality constraints (t1 ~R# t2) and (t1 ~N# t2) we use a different plan For unboxed equalities: - Generate a CoercionHole, a mutable variable just like a unification variable - Wrap the CoercionHole in a Wanted constraint; see TcRnTypes.TcEvDest - Use the CoercionHole in a Coercion, via HoleProv - Solve the constraint later - When solved, fill in the CoercionHole by side effect, instead of doing the let-binding thing The main reason for all this is that there may be no good place to let-bind the evidence for unboxed equalities: - We emit constraints for kind coercions, to be used to cast a type's kind. These coercions then must be used in types. Because they might appear in a top-level type, there is no place to bind these (unlifted) coercions in the usual way. - A coercion for (forall a. t1) ~ forall a. t2) will look like forall a. (coercion for t1~t2) But the coercion for (t1~t2) may mention 'a', and we don't have let-bindings within coercions. We could add them, but coercion holes are easier. Other notes about HoleCo: * INVARIANT: CoercionHole and HoleProv are used only during type checking, and should never appear in Core. Just like unification variables; a Type can contain a TcTyVar, but only during type checking. If, one day, we use type-level information to separate out forms that can appear during type-checking vs forms that can appear in core proper, holes in Core will be ruled out. * The Unique carried with a coercion hole is used solely for debugging. * Coercion holes can be compared for equality only like other coercions: only by looking at the types coerced. * We don't use holes for other evidence because other evidence wants to be /shared/. But coercions are entirely erased, so there's little benefit to sharing. Note [ProofIrrelProv] ~~~~~~~~~~~~~~~~~~~~~ A ProofIrrelProv is a coercion between coercions. For example: data G a where MkG :: G Bool In core, we get G :: * -> * MkG :: forall (a :: *). (a ~ Bool) -> G a Now, consider 'MkG -- that is, MkG used in a type -- and suppose we want a proof that ('MkG co1 a1) ~ ('MkG co2 a2). This will have to be TyConAppCo Nominal MkG [co3, co4] where co3 :: co1 ~ co2 co4 :: a1 ~ a2 Note that co1 :: a1 ~ Bool co2 :: a2 ~ Bool Here, co3 = UnivCo (ProofIrrelProv co5) Nominal (CoercionTy co1) (CoercionTy co2) where co5 :: (a1 ~ Bool) ~ (a2 ~ Bool) co5 = TyConAppCo Nominal (~) [<*>, <*>, co4, <Bool>] %************************************************************************ %* * Free variables of types and coercions %* * %************************************************************************ -} -- | Returns free variables of a type, including kind variables as -- a non-deterministic set. For type synonyms it does /not/ expand the -- synonym. tyCoVarsOfType :: Type -> TyCoVarSet tyCoVarsOfType ty = runFVSet $ tyCoVarsOfTypeAcc ty -- | `tyVarsOfType` that returns free variables of a type in a deterministic -- set. For explanation of why using `VarSet` is not deterministic see -- Note [Deterministic FV] in FV. tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet tyCoVarsOfTypeDSet ty = runFVDSet $ tyCoVarsOfTypeAcc ty -- | `tyVarsOfType` that returns free variables of a type in deterministic -- order. For explanation of why using `VarSet` is not deterministic see -- Note [Deterministic FV] in FV. tyCoVarsOfTypeList :: Type -> [TyCoVar] tyCoVarsOfTypeList ty = runFVList $ tyCoVarsOfTypeAcc ty -- | The worker for `tyVarsOfType` and `tyVarsOfTypeList`. -- The previous implementation used `unionVarSet` which is O(n+m) and can -- make the function quadratic. -- It's exported, so that it can be composed with -- other functions that compute free variables. -- See Note [FV naming conventions] in FV. -- -- Eta-expanded because that makes it run faster (apparently) tyCoVarsOfTypeAcc :: Type -> FV tyCoVarsOfTypeAcc (TyVarTy v) a b c = (oneVar v `unionFV` tyCoVarsOfTypeAcc (tyVarKind v)) a b c tyCoVarsOfTypeAcc (TyConApp _ tys) a b c = tyCoVarsOfTypesAcc tys a b c tyCoVarsOfTypeAcc (LitTy {}) a b c = noVars a b c tyCoVarsOfTypeAcc (AppTy fun arg) a b c = (tyCoVarsOfTypeAcc fun `unionFV` tyCoVarsOfTypeAcc arg) a b c tyCoVarsOfTypeAcc (ForAllTy bndr ty) a b c = tyCoVarsBndrAcc bndr (tyCoVarsOfTypeAcc ty) a b c tyCoVarsOfTypeAcc (CastTy ty co) a b c = (tyCoVarsOfTypeAcc ty `unionFV` tyCoVarsOfCoAcc co) a b c tyCoVarsOfTypeAcc (CoercionTy co) a b c = tyCoVarsOfCoAcc co a b c tyCoVarsBndrAcc :: TyBinder -> FV -> FV -- Free vars of (forall b. <thing with fvs>) tyCoVarsBndrAcc bndr fvs = delBinderVarFV bndr fvs `unionFV` tyCoVarsOfTypeAcc (binderType bndr) -- | Returns free variables of types, including kind variables as -- a non-deterministic set. For type synonyms it does /not/ expand the -- synonym. tyCoVarsOfTypes :: [Type] -> TyCoVarSet tyCoVarsOfTypes tys = runFVSet $ tyCoVarsOfTypesAcc tys -- | Returns free variables of types, including kind variables as -- a deterministic set. For type synonyms it does /not/ expand the -- synonym. tyCoVarsOfTypesDSet :: [Type] -> DTyCoVarSet tyCoVarsOfTypesDSet tys = runFVDSet $ tyCoVarsOfTypesAcc tys -- | Returns free variables of types, including kind variables as -- a deterministically ordered list. For type synonyms it does /not/ expand the -- synonym. tyCoVarsOfTypesList :: [Type] -> [TyCoVar] tyCoVarsOfTypesList tys = runFVList $ tyCoVarsOfTypesAcc tys tyCoVarsOfTypesAcc :: [Type] -> FV tyCoVarsOfTypesAcc (ty:tys) fv_cand in_scope acc = (tyCoVarsOfTypeAcc ty `unionFV` tyCoVarsOfTypesAcc tys) fv_cand in_scope acc tyCoVarsOfTypesAcc [] fv_cand in_scope acc = noVars fv_cand in_scope acc tyCoVarsOfCo :: Coercion -> TyCoVarSet tyCoVarsOfCo co = runFVSet $ tyCoVarsOfCoAcc co -- | Get a deterministic set of the vars free in a coercion tyCoVarsOfCoDSet :: Coercion -> DTyCoVarSet tyCoVarsOfCoDSet co = runFVDSet $ tyCoVarsOfCoAcc co tyCoVarsOfCoList :: Coercion -> [TyCoVar] tyCoVarsOfCoList co = runFVList $ tyCoVarsOfCoAcc co tyCoVarsOfCoAcc :: Coercion -> FV -- Extracts type and coercion variables from a coercion tyCoVarsOfCoAcc (Refl _ ty) fv_cand in_scope acc = tyCoVarsOfTypeAcc ty fv_cand in_scope acc tyCoVarsOfCoAcc (TyConAppCo _ _ cos) fv_cand in_scope acc = tyCoVarsOfCosAcc cos fv_cand in_scope acc tyCoVarsOfCoAcc (AppCo co arg) fv_cand in_scope acc = (tyCoVarsOfCoAcc co `unionFV` tyCoVarsOfCoAcc arg) fv_cand in_scope acc tyCoVarsOfCoAcc (ForAllCo tv kind_co co) fv_cand in_scope acc = (delFV tv (tyCoVarsOfCoAcc co) `unionFV` tyCoVarsOfCoAcc kind_co) fv_cand in_scope acc tyCoVarsOfCoAcc (CoVarCo v) fv_cand in_scope acc = (oneVar v `unionFV` tyCoVarsOfTypeAcc (varType v)) fv_cand in_scope acc tyCoVarsOfCoAcc (AxiomInstCo _ _ cos) fv_cand in_scope acc = tyCoVarsOfCosAcc cos fv_cand in_scope acc tyCoVarsOfCoAcc (UnivCo p _ t1 t2) fv_cand in_scope acc = (tyCoVarsOfProvAcc p `unionFV` tyCoVarsOfTypeAcc t1 `unionFV` tyCoVarsOfTypeAcc t2) fv_cand in_scope acc tyCoVarsOfCoAcc (SymCo co) fv_cand in_scope acc = tyCoVarsOfCoAcc co fv_cand in_scope acc tyCoVarsOfCoAcc (TransCo co1 co2) fv_cand in_scope acc = (tyCoVarsOfCoAcc co1 `unionFV` tyCoVarsOfCoAcc co2) fv_cand in_scope acc tyCoVarsOfCoAcc (NthCo _ co) fv_cand in_scope acc = tyCoVarsOfCoAcc co fv_cand in_scope acc tyCoVarsOfCoAcc (LRCo _ co) fv_cand in_scope acc = tyCoVarsOfCoAcc co fv_cand in_scope acc tyCoVarsOfCoAcc (InstCo co arg) fv_cand in_scope acc = (tyCoVarsOfCoAcc co `unionFV` tyCoVarsOfCoAcc arg) fv_cand in_scope acc tyCoVarsOfCoAcc (CoherenceCo c1 c2) fv_cand in_scope acc = (tyCoVarsOfCoAcc c1 `unionFV` tyCoVarsOfCoAcc c2) fv_cand in_scope acc tyCoVarsOfCoAcc (KindCo co) fv_cand in_scope acc = tyCoVarsOfCoAcc co fv_cand in_scope acc tyCoVarsOfCoAcc (SubCo co) fv_cand in_scope acc = tyCoVarsOfCoAcc co fv_cand in_scope acc tyCoVarsOfCoAcc (AxiomRuleCo _ cs) fv_cand in_scope acc = tyCoVarsOfCosAcc cs fv_cand in_scope acc tyCoVarsOfProv :: UnivCoProvenance -> TyCoVarSet tyCoVarsOfProv prov = runFVSet $ tyCoVarsOfProvAcc prov tyCoVarsOfProvAcc :: UnivCoProvenance -> FV tyCoVarsOfProvAcc UnsafeCoerceProv fv_cand in_scope acc = noVars fv_cand in_scope acc tyCoVarsOfProvAcc (PhantomProv co) fv_cand in_scope acc = tyCoVarsOfCoAcc co fv_cand in_scope acc tyCoVarsOfProvAcc (ProofIrrelProv co) fv_cand in_scope acc = tyCoVarsOfCoAcc co fv_cand in_scope acc tyCoVarsOfProvAcc (PluginProv _) fv_cand in_scope acc = noVars fv_cand in_scope acc tyCoVarsOfProvAcc (HoleProv _) fv_cand in_scope acc = noVars fv_cand in_scope acc tyCoVarsOfCos :: [Coercion] -> TyCoVarSet tyCoVarsOfCos cos = runFVSet $ tyCoVarsOfCosAcc cos tyCoVarsOfCosAcc :: [Coercion] -> FV tyCoVarsOfCosAcc [] fv_cand in_scope acc = noVars fv_cand in_scope acc tyCoVarsOfCosAcc (co:cos) fv_cand in_scope acc = (tyCoVarsOfCoAcc co `unionFV` tyCoVarsOfCosAcc cos) fv_cand in_scope acc coVarsOfType :: Type -> CoVarSet coVarsOfType (TyVarTy v) = coVarsOfType (tyVarKind v) coVarsOfType (TyConApp _ tys) = coVarsOfTypes tys coVarsOfType (LitTy {}) = emptyVarSet coVarsOfType (AppTy fun arg) = coVarsOfType fun `unionVarSet` coVarsOfType arg coVarsOfType (ForAllTy bndr ty) = coVarsOfType ty `delBinderVar` bndr `unionVarSet` coVarsOfType (binderType bndr) coVarsOfType (CastTy ty co) = coVarsOfType ty `unionVarSet` coVarsOfCo co coVarsOfType (CoercionTy co) = coVarsOfCo co coVarsOfTypes :: [Type] -> TyCoVarSet coVarsOfTypes tys = mapUnionVarSet coVarsOfType tys coVarsOfCo :: Coercion -> CoVarSet -- Extract *coercion* variables only. Tiresome to repeat the code, but easy. coVarsOfCo (Refl _ ty) = coVarsOfType ty coVarsOfCo (TyConAppCo _ _ args) = coVarsOfCos args coVarsOfCo (AppCo co arg) = coVarsOfCo co `unionVarSet` coVarsOfCo arg coVarsOfCo (ForAllCo tv kind_co co) = coVarsOfCo co `delVarSet` tv `unionVarSet` coVarsOfCo kind_co coVarsOfCo (CoVarCo v) = unitVarSet v `unionVarSet` coVarsOfType (varType v) coVarsOfCo (AxiomInstCo _ _ args) = coVarsOfCos args coVarsOfCo (UnivCo p _ t1 t2) = coVarsOfProv p `unionVarSet` coVarsOfTypes [t1, t2] coVarsOfCo (SymCo co) = coVarsOfCo co coVarsOfCo (TransCo co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2 coVarsOfCo (NthCo _ co) = coVarsOfCo co coVarsOfCo (LRCo _ co) = coVarsOfCo co coVarsOfCo (InstCo co arg) = coVarsOfCo co `unionVarSet` coVarsOfCo arg coVarsOfCo (CoherenceCo c1 c2) = coVarsOfCos [c1, c2] coVarsOfCo (KindCo co) = coVarsOfCo co coVarsOfCo (SubCo co) = coVarsOfCo co coVarsOfCo (AxiomRuleCo _ cs) = coVarsOfCos cs coVarsOfProv :: UnivCoProvenance -> CoVarSet coVarsOfProv UnsafeCoerceProv = emptyVarSet coVarsOfProv (PhantomProv co) = coVarsOfCo co coVarsOfProv (ProofIrrelProv co) = coVarsOfCo co coVarsOfProv (PluginProv _) = emptyVarSet coVarsOfProv (HoleProv _) = emptyVarSet coVarsOfCos :: [Coercion] -> CoVarSet coVarsOfCos cos = mapUnionVarSet coVarsOfCo cos -- | Add the kind variables free in the kinds of the tyvars in the given set. -- Returns a non-deterministic set. closeOverKinds :: TyVarSet -> TyVarSet closeOverKinds = runFVSet . closeOverKindsAcc . varSetElems -- | Given a list of tyvars returns a deterministic FV computation that -- returns the given tyvars with the kind variables free in the kinds of the -- given tyvars. closeOverKindsAcc :: [TyVar] -> FV closeOverKindsAcc tvs = mapUnionFV (tyCoVarsOfTypeAcc . tyVarKind) tvs `unionFV` someVars tvs -- | Add the kind variables free in the kinds of the tyvars in the given set. -- Returns a deterministic set. closeOverKindsDSet :: DTyVarSet -> DTyVarSet closeOverKindsDSet = runFVDSet . closeOverKindsAcc . dVarSetElems -- | Gets the free vars of a telescope, scoped over a given free var set. tyCoVarsOfTelescope :: [Var] -> TyCoVarSet -> TyCoVarSet tyCoVarsOfTelescope [] fvs = fvs tyCoVarsOfTelescope (v:vs) fvs = tyCoVarsOfTelescope vs fvs `delVarSet` v `unionVarSet` tyCoVarsOfType (varType v) {- %************************************************************************ %* * TyThing %* * %************************************************************************ Despite the fact that DataCon has to be imported via a hi-boot route, this module seems the right place for TyThing, because it's needed for funTyCon and all the types in TysPrim. Note [ATyCon for classes] ~~~~~~~~~~~~~~~~~~~~~~~~~ Both classes and type constructors are represented in the type environment as ATyCon. You can tell the difference, and get to the class, with isClassTyCon :: TyCon -> Bool tyConClass_maybe :: TyCon -> Maybe Class The Class and its associated TyCon have the same Name. -} -- | A global typecheckable-thing, essentially anything that has a name. -- Not to be confused with a 'TcTyThing', which is also a typecheckable -- thing but in the *local* context. See 'TcEnv' for how to retrieve -- a 'TyThing' given a 'Name'. data TyThing = AnId Id | AConLike ConLike | ATyCon TyCon -- TyCons and classes; see Note [ATyCon for classes] | ACoAxiom (CoAxiom Branched) deriving (Eq, Ord) instance Outputable TyThing where ppr = pprTyThing pprTyThing :: TyThing -> SDoc pprTyThing thing = pprTyThingCategory thing <+> quotes (ppr (getName thing)) pprTyThingCategory :: TyThing -> SDoc pprTyThingCategory (ATyCon tc) | isClassTyCon tc = text "Class" | otherwise = text "Type constructor" pprTyThingCategory (ACoAxiom _) = text "Coercion axiom" pprTyThingCategory (AnId _) = text "Identifier" pprTyThingCategory (AConLike (RealDataCon _)) = text "Data constructor" pprTyThingCategory (AConLike (PatSynCon _)) = text "Pattern synonym" instance NamedThing TyThing where -- Can't put this with the type getName (AnId id) = getName id -- decl, because the DataCon instance getName (ATyCon tc) = getName tc -- isn't visible there getName (ACoAxiom cc) = getName cc getName (AConLike cl) = getName cl {- %************************************************************************ %* * Substitutions Data type defined here to avoid unnecessary mutual recursion %* * %************************************************************************ -} -- | Type & coercion substitution -- -- #tcvsubst_invariant# -- The following invariants must hold of a 'TCvSubst': -- -- 1. The in-scope set is needed /only/ to -- guide the generation of fresh uniques -- -- 2. In particular, the /kind/ of the type variables in -- the in-scope set is not relevant -- -- 3. The substitution is only applied ONCE! This is because -- in general such application will not reach a fixed point. data TCvSubst = TCvSubst InScopeSet -- The in-scope type and kind variables TvSubstEnv -- Substitutes both type and kind variables CvSubstEnv -- Substitutes coercion variables -- See Note [Apply Once] -- and Note [Extending the TvSubstEnv] -- and Note [Substituting types and coercions] -- and Note [The substitution invariant] -- | A substitution of 'Type's for 'TyVar's -- and 'Kind's for 'KindVar's type TvSubstEnv = TyVarEnv Type -- A TvSubstEnv is used both inside a TCvSubst (with the apply-once -- invariant discussed in Note [Apply Once]), and also independently -- in the middle of matching, and unification (see Types.Unify) -- So you have to look at the context to know if it's idempotent or -- apply-once or whatever -- | A substitution of 'Coercion's for 'CoVar's type CvSubstEnv = CoVarEnv Coercion {- Note [Apply Once] ~~~~~~~~~~~~~~~~~ We use TCvSubsts to instantiate things, and we might instantiate forall a b. ty \with the types [a, b], or [b, a]. So the substitution might go [a->b, b->a]. A similar situation arises in Core when we find a beta redex like (/\ a /\ b -> e) b a Then we also end up with a substitution that permutes type variables. Other variations happen to; for example [a -> (a, b)]. **************************************************** *** So a TCvSubst must be applied precisely once *** **************************************************** A TCvSubst is not idempotent, but, unlike the non-idempotent substitution we use during unifications, it must not be repeatedly applied. Note [Extending the TvSubstEnv] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ See #tcvsubst_invariant# for the invariants that must hold. This invariant allows a short-cut when the subst envs are empty: if the TvSubstEnv and CvSubstEnv are empty --- i.e. (isEmptyTCvSubst subst) holds --- then (substTy subst ty) does nothing. For example, consider: (/\a. /\b:(a~Int). ...b..) Int We substitute Int for 'a'. The Unique of 'b' does not change, but nevertheless we add 'b' to the TvSubstEnv, because b's kind does change This invariant has several crucial consequences: * In substTyVarBndr, we need extend the TvSubstEnv - if the unique has changed - or if the kind has changed * In substTyVar, we do not need to consult the in-scope set; the TvSubstEnv is enough * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty Note [Substituting types and coercions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Types and coercions are mutually recursive, and either may have variables "belonging" to the other. Thus, every time we wish to substitute in a type, we may also need to substitute in a coercion, and vice versa. However, the constructor used to create type variables is distinct from that of coercion variables, so we carry two VarEnvs in a TCvSubst. Note that it would be possible to use the CoercionTy constructor to combine these environments, but that seems like a false economy. Note that the TvSubstEnv should *never* map a CoVar (built with the Id constructor) and the CvSubstEnv should *never* map a TyVar. Furthermore, the range of the TvSubstEnv should *never* include a type headed with CoercionTy. Note [The substitution invariant] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When calling (substTy subst ty) it should be the case that the in-scope set in the substitution is a superset of both: * The free vars of the range of the substitution * The free vars of ty minus the domain of the substitution If we want to substitute [a -> ty1, b -> ty2] I used to think it was enough to generate an in-scope set that includes fv(ty1,ty2). But that's not enough; we really should also take the free vars of the type we are substituting into! Example: (forall b. (a,b,x)) [a -> List b] Then if we use the in-scope set {b}, there is a danger we will rename the forall'd variable to 'x' by mistake, getting this: (forall x. (List b, x, x)) Breaking this invariant caused the bug from #11371. -} emptyTvSubstEnv :: TvSubstEnv emptyTvSubstEnv = emptyVarEnv emptyCvSubstEnv :: CvSubstEnv emptyCvSubstEnv = emptyVarEnv composeTCvSubstEnv :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv) -> (TvSubstEnv, CvSubstEnv) -- ^ @(compose env1 env2)(x)@ is @env1(env2(x))@; i.e. apply @env2@ then @env1@. -- It assumes that both are idempotent. -- Typically, @env1@ is the refinement to a base substitution @env2@ composeTCvSubstEnv in_scope (tenv1, cenv1) (tenv2, cenv2) = ( tenv1 `plusVarEnv` mapVarEnv (substTy subst1) tenv2 , cenv1 `plusVarEnv` mapVarEnv (substCo subst1) cenv2 ) -- First apply env1 to the range of env2 -- Then combine the two, making sure that env1 loses if -- both bind the same variable; that's why env1 is the -- *left* argument to plusVarEnv, because the right arg wins where subst1 = TCvSubst in_scope tenv1 cenv1 -- | Composes two substitutions, applying the second one provided first, -- like in function composition. composeTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst composeTCvSubst (TCvSubst is1 tenv1 cenv1) (TCvSubst is2 tenv2 cenv2) = TCvSubst is3 tenv3 cenv3 where is3 = is1 `unionInScope` is2 (tenv3, cenv3) = composeTCvSubstEnv is3 (tenv1, cenv1) (tenv2, cenv2) emptyTCvSubst :: TCvSubst emptyTCvSubst = TCvSubst emptyInScopeSet emptyTvSubstEnv emptyCvSubstEnv mkEmptyTCvSubst :: InScopeSet -> TCvSubst mkEmptyTCvSubst is = TCvSubst is emptyTvSubstEnv emptyCvSubstEnv isEmptyTCvSubst :: TCvSubst -> Bool -- See Note [Extending the TvSubstEnv] isEmptyTCvSubst (TCvSubst _ tenv cenv) = isEmptyVarEnv tenv && isEmptyVarEnv cenv mkTCvSubst :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> TCvSubst mkTCvSubst in_scope (tenv, cenv) = TCvSubst in_scope tenv cenv mkTvSubst :: InScopeSet -> TvSubstEnv -> TCvSubst -- ^ Mkae a TCvSubst with specified tyvar subst and empty covar subst mkTvSubst in_scope tenv = TCvSubst in_scope tenv emptyCvSubstEnv getTvSubstEnv :: TCvSubst -> TvSubstEnv getTvSubstEnv (TCvSubst _ env _) = env getCvSubstEnv :: TCvSubst -> CvSubstEnv getCvSubstEnv (TCvSubst _ _ env) = env getTCvInScope :: TCvSubst -> InScopeSet getTCvInScope (TCvSubst in_scope _ _) = in_scope isInScope :: Var -> TCvSubst -> Bool isInScope v (TCvSubst in_scope _ _) = v `elemInScopeSet` in_scope notElemTCvSubst :: Var -> TCvSubst -> Bool notElemTCvSubst v (TCvSubst _ tenv cenv) | isTyVar v = not (v `elemVarEnv` tenv) | otherwise = not (v `elemVarEnv` cenv) setTvSubstEnv :: TCvSubst -> TvSubstEnv -> TCvSubst setTvSubstEnv (TCvSubst in_scope _ cenv) tenv = TCvSubst in_scope tenv cenv setCvSubstEnv :: TCvSubst -> CvSubstEnv -> TCvSubst setCvSubstEnv (TCvSubst in_scope tenv _) cenv = TCvSubst in_scope tenv cenv zapTCvSubst :: TCvSubst -> TCvSubst zapTCvSubst (TCvSubst in_scope _ _) = TCvSubst in_scope emptyVarEnv emptyVarEnv extendTCvInScope :: TCvSubst -> Var -> TCvSubst extendTCvInScope (TCvSubst in_scope tenv cenv) var = TCvSubst (extendInScopeSet in_scope var) tenv cenv extendTCvInScopeList :: TCvSubst -> [Var] -> TCvSubst extendTCvInScopeList (TCvSubst in_scope tenv cenv) vars = TCvSubst (extendInScopeSetList in_scope vars) tenv cenv extendTCvInScopeSet :: TCvSubst -> VarSet -> TCvSubst extendTCvInScopeSet (TCvSubst in_scope tenv cenv) vars = TCvSubst (extendInScopeSetSet in_scope vars) tenv cenv extendTCvSubst :: TCvSubst -> TyCoVar -> Type -> TCvSubst extendTCvSubst subst v ty | isTyVar v = extendTvSubst subst v ty | CoercionTy co <- ty = extendCvSubst subst v co | otherwise = pprPanic "extendTCvSubst" (ppr v <+> text "|->" <+> ppr ty) extendTvSubst :: TCvSubst -> TyVar -> Type -> TCvSubst extendTvSubst (TCvSubst in_scope tenv cenv) tv ty = TCvSubst in_scope (extendVarEnv tenv tv ty) cenv extendTvSubstWithClone :: TCvSubst -> TyVar -> TyVar -> TCvSubst -- Adds a new tv -> tv mapping, /and/ extends the in-scope set extendTvSubstWithClone (TCvSubst in_scope tenv cenv) tv tv' = TCvSubst (extendInScopeSet in_scope tv') (extendVarEnv tenv tv (mkTyVarTy tv')) cenv extendCvSubst :: TCvSubst -> CoVar -> Coercion -> TCvSubst extendCvSubst (TCvSubst in_scope tenv cenv) v co = TCvSubst in_scope tenv (extendVarEnv cenv v co) extendCvSubstWithClone :: TCvSubst -> CoVar -> CoVar -> TCvSubst extendCvSubstWithClone (TCvSubst in_scope tenv cenv) cv cv' = TCvSubst (extendInScopeSet in_scope cv') tenv (extendVarEnv cenv cv (mkCoVarCo cv')) extendTvSubstAndInScope :: TCvSubst -> TyVar -> Type -> TCvSubst -- Also extends the in-scope set extendTvSubstAndInScope (TCvSubst in_scope tenv cenv) tv ty = TCvSubst (in_scope `extendInScopeSetSet` tyCoVarsOfType ty) (extendVarEnv tenv tv ty) cenv extendTvSubstList :: TCvSubst -> [Var] -> [Type] -> TCvSubst extendTvSubstList subst tvs tys = foldl2 extendTvSubst subst tvs tys extendTvSubstBinder :: TCvSubst -> TyBinder -> Type -> TCvSubst extendTvSubstBinder env (Anon {}) _ = env extendTvSubstBinder env (Named tv _) ty = extendTvSubst env tv ty unionTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst -- Works when the ranges are disjoint unionTCvSubst (TCvSubst in_scope1 tenv1 cenv1) (TCvSubst in_scope2 tenv2 cenv2) = ASSERT( not (tenv1 `intersectsVarEnv` tenv2) && not (cenv1 `intersectsVarEnv` cenv2) ) TCvSubst (in_scope1 `unionInScope` in_scope2) (tenv1 `plusVarEnv` tenv2) (cenv1 `plusVarEnv` cenv2) -- mkTvSubstPrs and zipTvSubst generate the in-scope set from -- the types given; but it's just a thunk so with a bit of luck -- it'll never be evaluated -- | Generates an in-scope set from the free variables in a list of types -- and a list of coercions mkTyCoInScopeSet :: [Type] -> [Coercion] -> InScopeSet mkTyCoInScopeSet tys cos = mkInScopeSet (tyCoVarsOfTypes tys `unionVarSet` tyCoVarsOfCos cos) -- | Generates the in-scope set for the 'TCvSubst' from the types in the incoming -- environment. No CoVars, please! zipTvSubst :: [TyVar] -> [Type] -> TCvSubst zipTvSubst tvs tys | debugIsOn , not (all isTyVar tvs) || length tvs /= length tys = pprTrace "zipTvSubst" (ppr tvs $$ ppr tys) emptyTCvSubst | otherwise = mkTvSubst (mkInScopeSet (tyCoVarsOfTypes tys)) tenv where tenv = zipTyEnv tvs tys -- | Generates the in-scope set for the 'TCvSubst' from the types in the incoming -- environment. No TyVars, please! zipCvSubst :: [CoVar] -> [Coercion] -> TCvSubst zipCvSubst cvs cos | debugIsOn , not (all isCoVar cvs) || length cvs /= length cos = pprTrace "zipCvSubst" (ppr cvs $$ ppr cos) emptyTCvSubst | otherwise = TCvSubst (mkInScopeSet (tyCoVarsOfCos cos)) emptyTvSubstEnv cenv where cenv = zipCoEnv cvs cos -- | Create a TCvSubst combining the binders and types provided. -- NB: It is specifically OK if the lists are of different lengths. zipTyBinderSubst :: [TyBinder] -> [Type] -> TCvSubst zipTyBinderSubst bndrs tys = mkTvSubst is tenv where is = mkInScopeSet (tyCoVarsOfTypes tys) tenv = mkVarEnv [ (tv, ty) | (Named tv _, ty) <- zip bndrs tys ] -- | Generates the in-scope set for the 'TCvSubst' from the types in the -- incoming environment. No CoVars, please! mkTvSubstPrs :: [(TyVar, Type)] -> TCvSubst mkTvSubstPrs prs = ASSERT2( onlyTyVarsAndNoCoercionTy, text "prs" <+> ppr prs ) mkTvSubst in_scope tenv where tenv = mkVarEnv prs in_scope = mkInScopeSet $ tyCoVarsOfTypes $ map snd prs onlyTyVarsAndNoCoercionTy = and [ isTyVar tv && not (isCoercionTy ty) | (tv, ty) <- prs ] zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv zipTyEnv tyvars tys = ASSERT( all (not . isCoercionTy) tys ) mkVarEnv (zipEqual "zipTyEnv" tyvars tys) -- There used to be a special case for when -- ty == TyVarTy tv -- (a not-uncommon case) in which case the substitution was dropped. -- But the type-tidier changes the print-name of a type variable without -- changing the unique, and that led to a bug. Why? Pre-tidying, we had -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype. -- And it happened that t was the type variable of the class. Post-tiding, -- it got turned into {Foo t2}. The ext-core printer expanded this using -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique, -- and so generated a rep type mentioning t not t2. -- -- Simplest fix is to nuke the "optimisation" zipCoEnv :: [CoVar] -> [Coercion] -> CvSubstEnv zipCoEnv cvs cos = mkVarEnv (zipEqual "zipCoEnv" cvs cos) instance Outputable TCvSubst where ppr (TCvSubst ins tenv cenv) = brackets $ sep[ text "TCvSubst", nest 2 (text "In scope:" <+> ppr ins), nest 2 (text "Type env:" <+> ppr tenv), nest 2 (text "Co env:" <+> ppr cenv) ] {- %************************************************************************ %* * Performing type or kind substitutions %* * %************************************************************************ Note [Sym and ForAllCo] ~~~~~~~~~~~~~~~~~~~~~~~ In OptCoercion, we try to push "sym" out to the leaves of a coercion. But, how do we push sym into a ForAllCo? It's a little ugly. Here is the typing rule: h : k1 ~# k2 (tv : k1) |- g : ty1 ~# ty2 ---------------------------- ForAllCo tv h g : (ForAllTy (tv : k1) ty1) ~# (ForAllTy (tv : k2) (ty2[tv |-> tv |> sym h])) Here is what we want: ForAllCo tv h' g' : (ForAllTy (tv : k2) (ty2[tv |-> tv |> sym h])) ~# (ForAllTy (tv : k1) ty1) Because the kinds of the type variables to the right of the colon are the kinds coerced by h', we know (h' : k2 ~# k1). Thus, (h' = sym h). Now, we can rewrite ty1 to be (ty1[tv |-> tv |> sym h' |> h']). We thus want ForAllCo tv h' g' : (ForAllTy (tv : k2) (ty2[tv |-> tv |> h'])) ~# (ForAllTy (tv : k1) (ty1[tv |-> tv |> h'][tv |-> tv |> sym h'])) We thus see that we want g' : ty2[tv |-> tv |> h'] ~# ty1[tv |-> tv |> h'] and thus g' = sym (g[tv |-> tv |> h']). Putting it all together, we get this: sym (ForAllCo tv h g) ==> ForAllCo tv (sym h) (sym g[tv |-> tv |> sym h]) -} -- | Type substitution, see 'zipTvSubst' substTyWith :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif [TyVar] -> [Type] -> Type -> Type -- Works only if the domain of the substitution is a -- superset of the type being substituted into substTyWith tvs tys = ASSERT( length tvs == length tys ) substTy (zipTvSubst tvs tys) -- | Type substitution, see 'zipTvSubst'. Disables sanity checks. -- The problems that the sanity checks in substTy catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substTyUnchecked to -- substTy and remove this function. Please don't use in new code. substTyWithUnchecked :: [TyVar] -> [Type] -> Type -> Type substTyWithUnchecked tvs tys = ASSERT( length tvs == length tys ) substTyUnchecked (zipTvSubst tvs tys) -- | Substitute tyvars within a type using a known 'InScopeSet'. -- Pre-condition: the 'in_scope' set should satisfy Note [The substitution -- invariant]; specifically it should include the free vars of 'tys', -- and of 'ty' minus the domain of the subst. substTyWithInScope :: InScopeSet -> [TyVar] -> [Type] -> Type -> Type substTyWithInScope in_scope tvs tys ty = ASSERT( length tvs == length tys ) substTy (mkTvSubst in_scope tenv) ty where tenv = zipTyEnv tvs tys -- | Coercion substitution, see 'zipTvSubst' substCoWith :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif [TyVar] -> [Type] -> Coercion -> Coercion substCoWith tvs tys = ASSERT( length tvs == length tys ) substCo (zipTvSubst tvs tys) -- | Coercion substitution, see 'zipTvSubst'. Disables sanity checks. -- The problems that the sanity checks in substCo catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substCoUnchecked to -- substCo and remove this function. Please don't use in new code. substCoWithUnchecked :: [TyVar] -> [Type] -> Coercion -> Coercion substCoWithUnchecked tvs tys = ASSERT( length tvs == length tys ) substCoUnchecked (zipTvSubst tvs tys) -- | Substitute covars within a type substTyWithCoVars :: [CoVar] -> [Coercion] -> Type -> Type substTyWithCoVars cvs cos = substTy (zipCvSubst cvs cos) -- | Type substitution, see 'zipTvSubst' substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type] substTysWith tvs tys = ASSERT( length tvs == length tys ) substTys (zipTvSubst tvs tys) -- | Type substitution, see 'zipTvSubst' substTysWithCoVars :: [CoVar] -> [Coercion] -> [Type] -> [Type] substTysWithCoVars cvs cos = ASSERT( length cvs == length cos ) substTys (zipCvSubst cvs cos) -- | Type substitution using 'Binder's. Anonymous binders -- simply ignore their matching type. substTyWithBinders :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif [TyBinder] -> [Type] -> Type -> Type substTyWithBinders bndrs tys = ASSERT( length bndrs == length tys ) substTy (zipTyBinderSubst bndrs tys) -- | Type substitution using 'Binder's disabling the sanity checks. -- Anonymous binders simply ignore their matching type. -- The problems that the sanity checks in substTy catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substTyUnchecked to -- substTy and remove this function. Please don't use in new code. substTyWithBindersUnchecked :: [TyBinder] -> [Type] -> Type -> Type substTyWithBindersUnchecked bndrs tys = ASSERT( length bndrs == length tys ) substTyUnchecked (zipTyBinderSubst bndrs tys) -- | Substitute within a 'Type' after adding the free variables of the type -- to the in-scope set. This is useful for the case when the free variables -- aren't already in the in-scope set or easily available. -- See also Note [The substitution invariant]. substTyAddInScope :: TCvSubst -> Type -> Type substTyAddInScope subst ty = substTy (extendTCvInScopeSet subst $ tyCoVarsOfType ty) ty -- | When calling `substTy` it should be the case that the in-scope set in -- the substitution is a superset of the free vars of the range of the -- substitution. -- See also Note [The substitution invariant]. isValidTCvSubst :: TCvSubst -> Bool isValidTCvSubst (TCvSubst in_scope tenv cenv) = (tenvFVs `varSetInScope` in_scope) && (cenvFVs `varSetInScope` in_scope) where tenvFVs = tyCoVarsOfTypes $ varEnvElts tenv cenvFVs = tyCoVarsOfCos $ varEnvElts cenv -- | This checks if the substitution satisfies the invariant from -- Note [The substitution invariant]. checkValidSubst :: #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif TCvSubst -> [Type] -> [Coercion] -> a -> a checkValidSubst subst@(TCvSubst in_scope tenv cenv) tys cos a = ASSERT2( isValidTCvSubst subst, text "in_scope" <+> ppr in_scope $$ text "tenv" <+> ppr tenv $$ text "tenvFVs" <+> ppr (tyCoVarsOfTypes $ varEnvElts tenv) $$ text "cenv" <+> ppr cenv $$ text "cenvFVs" <+> ppr (tyCoVarsOfCos $ varEnvElts cenv) $$ text "tys" <+> ppr tys $$ text "cos" <+> ppr cos ) ASSERT2( tysCosFVsInScope, text "in_scope" <+> ppr in_scope $$ text "tenv" <+> ppr tenv $$ text "cenv" <+> ppr cenv $$ text "tys" <+> ppr tys $$ text "cos" <+> ppr cos $$ text "needInScope" <+> ppr needInScope ) a where substDomain = varEnvKeys tenv ++ varEnvKeys cenv needInScope = (tyCoVarsOfTypes tys `unionVarSet` tyCoVarsOfCos cos) `delListFromUFM_Directly` substDomain tysCosFVsInScope = needInScope `varSetInScope` in_scope -- | Substitute within a 'Type' -- The substitution has to satisfy the invariants described in -- Note [The substitution invariant]. substTy :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif TCvSubst -> Type -> Type substTy subst ty | isEmptyTCvSubst subst = ty | otherwise = checkValidSubst subst [ty] [] $ subst_ty subst ty -- | Substitute within a 'Type' disabling the sanity checks. -- The problems that the sanity checks in substTy catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substTyUnchecked to -- substTy and remove this function. Please don't use in new code. substTyUnchecked :: TCvSubst -> Type -> Type substTyUnchecked subst ty | isEmptyTCvSubst subst = ty | otherwise = subst_ty subst ty -- | Substitute within several 'Type's -- The substitution has to satisfy the invariants described in -- Note [The substitution invariant]. substTys :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif TCvSubst -> [Type] -> [Type] substTys subst tys | isEmptyTCvSubst subst = tys | otherwise = checkValidSubst subst tys [] $ map (subst_ty subst) tys -- | Substitute within several 'Type's disabling the sanity checks. -- The problems that the sanity checks in substTys catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substTysUnchecked to -- substTys and remove this function. Please don't use in new code. substTysUnchecked :: TCvSubst -> [Type] -> [Type] substTysUnchecked subst tys | isEmptyTCvSubst subst = tys | otherwise = map (subst_ty subst) tys -- | Substitute within a 'ThetaType' -- The substitution has to satisfy the invariants described in -- Note [The substitution invariant]. substTheta :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif TCvSubst -> ThetaType -> ThetaType substTheta = substTys -- | Substitute within a 'ThetaType' disabling the sanity checks. -- The problems that the sanity checks in substTys catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substThetaUnchecked to -- substTheta and remove this function. Please don't use in new code. substThetaUnchecked :: TCvSubst -> ThetaType -> ThetaType substThetaUnchecked = substTysUnchecked subst_ty :: TCvSubst -> Type -> Type -- subst_ty is the main workhorse for type substitution -- -- Note that the in_scope set is poked only if we hit a forall -- so it may often never be fully computed subst_ty subst ty = go ty where go (TyVarTy tv) = substTyVar subst tv go (AppTy fun arg) = mkAppTy (go fun) $! (go arg) -- The mkAppTy smart constructor is important -- we might be replacing (a Int), represented with App -- by [Int], represented with TyConApp go (TyConApp tc tys) = let args = map go tys in args `seqList` TyConApp tc args go (ForAllTy (Anon arg) res) = (ForAllTy $! (Anon $! go arg)) $! go res go (ForAllTy (Named tv vis) ty) = case substTyVarBndrUnchecked subst tv of (subst', tv') -> (ForAllTy $! ((Named $! tv') vis)) $! (subst_ty subst' ty) go (LitTy n) = LitTy $! n go (CastTy ty co) = (CastTy $! (go ty)) $! (subst_co subst co) go (CoercionTy co) = CoercionTy $! (subst_co subst co) substTyVar :: TCvSubst -> TyVar -> Type substTyVar (TCvSubst _ tenv _) tv = ASSERT( isTyVar tv ) case lookupVarEnv tenv tv of Just ty -> ty Nothing -> TyVarTy tv substTyVars :: TCvSubst -> [TyVar] -> [Type] substTyVars subst = map $ substTyVar subst lookupTyVar :: TCvSubst -> TyVar -> Maybe Type -- See Note [Extending the TCvSubst] lookupTyVar (TCvSubst _ tenv _) tv = ASSERT( isTyVar tv ) lookupVarEnv tenv tv -- | Substitute within a 'Coercion' -- The substitution has to satisfy the invariants described in -- Note [The substitution invariant]. substCo :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif TCvSubst -> Coercion -> Coercion substCo subst co | isEmptyTCvSubst subst = co | otherwise = checkValidSubst subst [] [co] $ subst_co subst co -- | Substitute within a 'Coercion' disabling sanity checks. -- The problems that the sanity checks in substCo catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substCoUnchecked to -- substCo and remove this function. Please don't use in new code. substCoUnchecked :: TCvSubst -> Coercion -> Coercion substCoUnchecked subst co | isEmptyTCvSubst subst = co | otherwise = subst_co subst co -- | Substitute within several 'Coercion's -- The substitution has to satisfy the invariants described in -- Note [The substitution invariant]. substCos :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif TCvSubst -> [Coercion] -> [Coercion] substCos subst cos | isEmptyTCvSubst subst = cos | otherwise = checkValidSubst subst [] cos $ map (subst_co subst) cos subst_co :: TCvSubst -> Coercion -> Coercion subst_co subst co = go co where go_ty :: Type -> Type go_ty = subst_ty subst go :: Coercion -> Coercion go (Refl r ty) = mkReflCo r $! go_ty ty go (TyConAppCo r tc args)= let args' = map go args in args' `seqList` mkTyConAppCo r tc args' go (AppCo co arg) = (mkAppCo $! go co) $! go arg go (ForAllCo tv kind_co co) = case substForAllCoBndrUnchecked subst tv kind_co of { (subst', tv', kind_co') -> ((mkForAllCo $! tv') $! kind_co') $! subst_co subst' co } go (CoVarCo cv) = substCoVar subst cv go (AxiomInstCo con ind cos) = mkAxiomInstCo con ind $! map go cos go (UnivCo p r t1 t2) = (((mkUnivCo $! go_prov p) $! r) $! (go_ty t1)) $! (go_ty t2) go (SymCo co) = mkSymCo $! (go co) go (TransCo co1 co2) = (mkTransCo $! (go co1)) $! (go co2) go (NthCo d co) = mkNthCo d $! (go co) go (LRCo lr co) = mkLRCo lr $! (go co) go (InstCo co arg) = (mkInstCo $! (go co)) $! go arg go (CoherenceCo co1 co2) = (mkCoherenceCo $! (go co1)) $! (go co2) go (KindCo co) = mkKindCo $! (go co) go (SubCo co) = mkSubCo $! (go co) go (AxiomRuleCo c cs) = let cs1 = map go cs in cs1 `seqList` AxiomRuleCo c cs1 go_prov UnsafeCoerceProv = UnsafeCoerceProv go_prov (PhantomProv kco) = PhantomProv (go kco) go_prov (ProofIrrelProv kco) = ProofIrrelProv (go kco) go_prov p@(PluginProv _) = p go_prov p@(HoleProv _) = p -- NB: this last case is a little suspicious, but we need it. Originally, -- there was a panic here, but it triggered from deeplySkolemise. Because -- we only skolemise tyvars that are manually bound, this operation makes -- sense, even over a coercion with holes. substForAllCoBndr :: TCvSubst -> TyVar -> Coercion -> (TCvSubst, TyVar, Coercion) substForAllCoBndr subst = substForAllCoBndrCallback False (substCo subst) subst -- | Like 'substForAllCoBndr', but disables sanity checks. -- The problems that the sanity checks in substCo catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substCoUnchecked to -- substCo and remove this function. Please don't use in new code. substForAllCoBndrUnchecked :: TCvSubst -> TyVar -> Coercion -> (TCvSubst, TyVar, Coercion) substForAllCoBndrUnchecked subst = substForAllCoBndrCallback False (substCoUnchecked subst) subst -- See Note [Sym and ForAllCo] substForAllCoBndrCallback :: Bool -- apply sym to binder? -> (Coercion -> Coercion) -- transformation to kind co -> TCvSubst -> TyVar -> Coercion -> (TCvSubst, TyVar, Coercion) substForAllCoBndrCallback sym sco (TCvSubst in_scope tenv cenv) old_var old_kind_co = ( TCvSubst (in_scope `extendInScopeSet` new_var) new_env cenv , new_var, new_kind_co ) where new_env | no_change && not sym = delVarEnv tenv old_var | sym = extendVarEnv tenv old_var $ TyVarTy new_var `CastTy` new_kind_co | otherwise = extendVarEnv tenv old_var (TyVarTy new_var) no_kind_change = isEmptyVarSet (tyCoVarsOfCo old_kind_co) no_change = no_kind_change && (new_var == old_var) new_kind_co | no_kind_change = old_kind_co | otherwise = sco old_kind_co Pair new_ki1 _ = coercionKind new_kind_co new_var = uniqAway in_scope (setTyVarKind old_var new_ki1) substCoVar :: TCvSubst -> CoVar -> Coercion substCoVar (TCvSubst _ _ cenv) cv = case lookupVarEnv cenv cv of Just co -> co Nothing -> CoVarCo cv substCoVars :: TCvSubst -> [CoVar] -> [Coercion] substCoVars subst cvs = map (substCoVar subst) cvs lookupCoVar :: TCvSubst -> Var -> Maybe Coercion lookupCoVar (TCvSubst _ _ cenv) v = lookupVarEnv cenv v substTyVarBndr :: -- CallStack wasn't present in GHC 7.10.1, disable callstacks in stage 1 #if __GLASGOW_HASKELL__ > 710 (?callStack :: CallStack) => #endif TCvSubst -> TyVar -> (TCvSubst, TyVar) substTyVarBndr = substTyVarBndrCallback substTy -- | Like 'substTyVarBndr' but disables sanity checks. -- The problems that the sanity checks in substTy catch are described in -- Note [The substitution invariant]. -- The goal of #11371 is to migrate all the calls of substTyUnchecked to -- substTy and remove this function. Please don't use in new code. substTyVarBndrUnchecked :: TCvSubst -> TyVar -> (TCvSubst, TyVar) substTyVarBndrUnchecked = substTyVarBndrCallback substTyUnchecked -- | Substitute a tyvar in a binding position, returning an -- extended subst and a new tyvar. substTyVarBndrCallback :: (TCvSubst -> Type -> Type) -- ^ the subst function -> TCvSubst -> TyVar -> (TCvSubst, TyVar) substTyVarBndrCallback subst_fn subst@(TCvSubst in_scope tenv cenv) old_var = ASSERT2( _no_capture, pprTvBndr old_var $$ pprTvBndr new_var $$ ppr subst ) ASSERT( isTyVar old_var ) (TCvSubst (in_scope `extendInScopeSet` new_var) new_env cenv, new_var) where new_env | no_change = delVarEnv tenv old_var | otherwise = extendVarEnv tenv old_var (TyVarTy new_var) _no_capture = not (new_var `elemVarSet` tyCoVarsOfTypes (varEnvElts tenv)) -- Assertion check that we are not capturing something in the substitution old_ki = tyVarKind old_var no_kind_change = isEmptyVarSet (tyCoVarsOfType old_ki) -- verify that kind is closed no_change = no_kind_change && (new_var == old_var) -- no_change means that the new_var is identical in -- all respects to the old_var (same unique, same kind) -- See Note [Extending the TCvSubst] -- -- In that case we don't need to extend the substitution -- to map old to new. But instead we must zap any -- current substitution for the variable. For example: -- (\x.e) with id_subst = [x |-> e'] -- Here we must simply zap the substitution for x new_var | no_kind_change = uniqAway in_scope old_var | otherwise = uniqAway in_scope $ setTyVarKind old_var (subst_fn subst old_ki) -- The uniqAway part makes sure the new variable is not already in scope substCoVarBndr :: TCvSubst -> CoVar -> (TCvSubst, CoVar) substCoVarBndr = substCoVarBndrCallback False substTy substCoVarBndrCallback :: Bool -- apply "sym" to the covar? -> (TCvSubst -> Type -> Type) -> TCvSubst -> CoVar -> (TCvSubst, CoVar) substCoVarBndrCallback sym subst_fun subst@(TCvSubst in_scope tenv cenv) old_var = ASSERT( isCoVar old_var ) (TCvSubst (in_scope `extendInScopeSet` new_var) tenv new_cenv, new_var) where -- When we substitute (co :: t1 ~ t2) we may get the identity (co :: t ~ t) -- In that case, mkCoVarCo will return a ReflCoercion, and -- we want to substitute that (not new_var) for old_var new_co = (if sym then mkSymCo else id) $ mkCoVarCo new_var no_kind_change = isEmptyVarSet (tyCoVarsOfTypes [t1, t2]) no_change = new_var == old_var && not (isReflCo new_co) && no_kind_change new_cenv | no_change = delVarEnv cenv old_var | otherwise = extendVarEnv cenv old_var new_co new_var = uniqAway in_scope subst_old_var subst_old_var = mkCoVar (varName old_var) new_var_type (_, _, t1, t2, role) = coVarKindsTypesRole old_var t1' = subst_fun subst t1 t2' = subst_fun subst t2 new_var_type = uncurry (mkCoercionType role) (if sym then (t2', t1') else (t1', t2')) -- It's important to do the substitution for coercions, -- because they can have free type variables cloneTyVarBndr :: TCvSubst -> TyVar -> Unique -> (TCvSubst, TyVar) cloneTyVarBndr subst@(TCvSubst in_scope tv_env cv_env) tv uniq = ASSERT2( isTyVar tv, ppr tv ) -- I think it's only called on TyVars (TCvSubst (extendInScopeSet in_scope tv') (extendVarEnv tv_env tv (mkTyVarTy tv')) cv_env, tv') where old_ki = tyVarKind tv no_kind_change = isEmptyVarSet (tyCoVarsOfType old_ki) -- verify that kind is closed tv1 | no_kind_change = tv | otherwise = setTyVarKind tv (substTy subst old_ki) tv' = setVarUnique tv1 uniq cloneTyVarBndrs :: TCvSubst -> [TyVar] -> UniqSupply -> (TCvSubst, [TyVar]) cloneTyVarBndrs subst [] _usupply = (subst, []) cloneTyVarBndrs subst (t:ts) usupply = (subst'', tv:tvs) where (uniq, usupply') = takeUniqFromSupply usupply (subst' , tv ) = cloneTyVarBndr subst t uniq (subst'', tvs) = cloneTyVarBndrs subst' ts usupply' {- %************************************************************************ %* * Pretty-printing types Defined very early because of debug printing in assertions %* * %************************************************************************ @pprType@ is the standard @Type@ printer; the overloaded @ppr@ function is defined to use this. @pprParendType@ is the same, except it puts parens around the type, except for the atomic cases. @pprParendType@ works just by setting the initial context precedence very high. Note [Precedence in types] ~~~~~~~~~~~~~~~~~~~~~~~~~~ We don't keep the fixity of type operators in the operator. So the pretty printer operates the following precedene structre: Type constructor application binds more tightly than Operator applications which bind more tightly than Function arrow So we might see a :+: T b -> c meaning (a :+: (T b)) -> c Maybe operator applications should bind a bit less tightly? Anyway, that's the current story, and it is used consistently for Type and HsType -} data TyPrec -- See Note [Prededence in types] = TopPrec -- No parens | FunPrec -- Function args; no parens for tycon apps | TyOpPrec -- Infix operator | TyConPrec -- Tycon args; no parens for atomic deriving( Eq, Ord ) maybeParen :: TyPrec -> TyPrec -> SDoc -> SDoc maybeParen ctxt_prec inner_prec pretty | ctxt_prec < inner_prec = pretty | otherwise = parens pretty ------------------ {- Note [Defaulting RuntimeRep variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ RuntimeRep variables are considered by many (most?) users to be little more than syntactic noise. When the notion was introduced there was a signficant and understandable push-back from those with pedagogy in mind, which argued that RuntimeRep variables would throw a wrench into nearly any teach approach since they appear in even the lowly ($) function's type, ($) :: forall (w :: RuntimeRep) a (b :: TYPE w). (a -> b) -> a -> b which is significantly less readable than its non RuntimeRep-polymorphic type of ($) :: (a -> b) -> a -> b Moreover, unboxed types don't appear all that often in run-of-the-mill Haskell programs, so it makes little sense to make all users pay this syntactic overhead. For this reason it was decided that we would hide RuntimeRep variables for now (see #11549). We do this by defaulting all type variables of kind RuntimeRep to PtrLiftedRep. This is done in a pass right before pretty-printing (defaultRuntimeRepVars, controlled by -fprint-explicit-runtime-reps) -} -- | Default 'RuntimeRep' variables to 'LiftedPtr'. e.g. -- -- @ -- ($) :: forall (r :: GHC.Types.RuntimeRep) a (b :: TYPE r). -- (a -> b) -> a -> b -- @ -- -- turns in to, -- -- @ ($) :: forall a (b :: *). (a -> b) -> a -> b @ -- -- We do this to prevent RuntimeRep variables from incurring a significant -- syntactic overhead in otherwise simple type signatures (e.g. ($)). See -- Note [Defaulting RuntimeRep variables] and #11549 for further discussion. -- defaultRuntimeRepVars :: Type -> Type defaultRuntimeRepVars = defaultRuntimeRepVars' emptyVarSet defaultRuntimeRepVars' :: TyVarSet -- ^ the binders which we should default -> Type -> Type -- TODO: Eventually we should just eliminate the Type pretty-printer -- entirely and simply use IfaceType; this task is tracked as #11660. defaultRuntimeRepVars' subs (ForAllTy (Named var vis) ty) | isRuntimeRepVar var = let subs' = extendVarSet subs var in defaultRuntimeRepVars' subs' ty | otherwise = let var' = var { varType = defaultRuntimeRepVars' subs (varType var) } in ForAllTy (Named var' vis) (defaultRuntimeRepVars' subs ty) defaultRuntimeRepVars' subs (ForAllTy (Anon kind) ty) = ForAllTy (Anon $ defaultRuntimeRepVars' subs kind) (defaultRuntimeRepVars' subs ty) defaultRuntimeRepVars' subs (TyVarTy var) | var `elemVarSet` subs = ptrRepLiftedTy defaultRuntimeRepVars' subs (TyConApp tc args) = TyConApp tc $ map (defaultRuntimeRepVars' subs) args defaultRuntimeRepVars' subs (AppTy x y) = defaultRuntimeRepVars' subs x `AppTy` defaultRuntimeRepVars' subs y defaultRuntimeRepVars' subs (CastTy ty co) = CastTy (defaultRuntimeRepVars' subs ty) co defaultRuntimeRepVars' _ other = other eliminateRuntimeRep :: (Type -> SDoc) -> Type -> SDoc eliminateRuntimeRep f ty = sdocWithDynFlags $ \dflags -> if gopt Opt_PrintExplicitRuntimeReps dflags then f ty else f (defaultRuntimeRepVars ty) pprType, pprParendType :: Type -> SDoc pprType ty = eliminateRuntimeRep (ppr_type TopPrec) ty pprParendType ty = eliminateRuntimeRep (ppr_type TyConPrec) ty pprTyLit :: TyLit -> SDoc pprTyLit = ppr_tylit TopPrec pprKind, pprParendKind :: Kind -> SDoc pprKind = pprType pprParendKind = pprParendType ------------ pprClassPred :: Class -> [Type] -> SDoc pprClassPred clas tys = pprTypeApp (classTyCon clas) tys ------------ pprTheta :: ThetaType -> SDoc pprTheta [pred] = ppr_type TopPrec pred -- I'm in two minds about this pprTheta theta = parens (sep (punctuate comma (map (ppr_type TopPrec) theta))) pprThetaArrowTy :: ThetaType -> SDoc pprThetaArrowTy [] = empty pprThetaArrowTy [pred] = ppr_type TyOpPrec pred <+> darrow -- TyOpPrec: Num a => a -> a does not need parens -- bug (a :~: b) => a -> b currently does -- Trac # 9658 pprThetaArrowTy preds = parens (fsep (punctuate comma (map (ppr_type TopPrec) preds))) <+> darrow -- Notice 'fsep' here rather that 'sep', so that -- type contexts don't get displayed in a giant column -- Rather than -- instance (Eq a, -- Eq b, -- Eq c, -- Eq d, -- Eq e, -- Eq f, -- Eq g, -- Eq h, -- Eq i, -- Eq j, -- Eq k, -- Eq l) => -- Eq (a, b, c, d, e, f, g, h, i, j, k, l) -- we get -- -- instance (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, -- Eq j, Eq k, Eq l) => -- Eq (a, b, c, d, e, f, g, h, i, j, k, l) ------------------ instance Outputable Type where ppr ty = pprType ty instance Outputable TyLit where ppr = pprTyLit ------------------ -- OK, here's the main printer ppr_type :: TyPrec -> Type -> SDoc ppr_type _ (TyVarTy tv) = ppr_tvar tv ppr_type p (TyConApp tc tys) = pprTyTcApp p tc tys ppr_type p (LitTy l) = ppr_tylit p l ppr_type p ty@(ForAllTy {}) = ppr_forall_type p ty ppr_type p (AppTy t1 t2) = if_print_coercions ppr_app_ty (case split_app_tys t1 [t2] of (CastTy head _, args) -> ppr_type p (mk_app_tys head args) _ -> ppr_app_ty) where ppr_app_ty = maybeParen p TyConPrec $ ppr_type FunPrec t1 <+> ppr_type TyConPrec t2 split_app_tys (AppTy ty1 ty2) args = split_app_tys ty1 (ty2:args) split_app_tys head args = (head, args) mk_app_tys (TyConApp tc tys1) tys2 = TyConApp tc (tys1 ++ tys2) mk_app_tys ty1 tys2 = foldl AppTy ty1 tys2 ppr_type p (CastTy ty co) = if_print_coercions (parens (ppr_type TopPrec ty <+> text "|>" <+> ppr co)) (ppr_type p ty) ppr_type _ (CoercionTy co) = if_print_coercions (parens (ppr co)) (text "<>") ppr_forall_type :: TyPrec -> Type -> SDoc ppr_forall_type p ty = maybeParen p FunPrec $ sdocWithDynFlags $ \dflags -> ppr_sigma_type dflags True ty -- True <=> we always print the foralls on *nested* quantifiers -- Opt_PrintExplicitForalls only affects top-level quantifiers ppr_tvar :: TyVar -> SDoc ppr_tvar tv -- Note [Infix type variables] = parenSymOcc (getOccName tv) (ppr tv) ppr_tylit :: TyPrec -> TyLit -> SDoc ppr_tylit _ tl = case tl of NumTyLit n -> integer n StrTyLit s -> text (show s) if_print_coercions :: SDoc -- if printing coercions -> SDoc -- otherwise -> SDoc if_print_coercions yes no = sdocWithDynFlags $ \dflags -> getPprStyle $ \style -> if gopt Opt_PrintExplicitCoercions dflags || dumpStyle style || debugStyle style then yes else no ------------------- ppr_sigma_type :: DynFlags -> Bool -- ^ True <=> Show the foralls unconditionally -> Type -> SDoc -- Suppose we have (forall a. Show a => forall b. a -> b). When we're not -- printing foralls, we want to drop both the (forall a) and the (forall b). -- This logic does so. ppr_sigma_type dflags False orig_ty | not (gopt Opt_PrintExplicitForalls dflags) , all (isEmptyVarSet . tyCoVarsOfType . binderType) named -- See Note [When to print foralls] = sep [ pprThetaArrowTy (map binderType ctxt) , pprArrowChain TopPrec (ppr_fun_tail tau) ] where (invis_bndrs, tau) = split [] orig_ty (named, ctxt) = partition isNamedBinder invis_bndrs split acc (ForAllTy bndr ty) | isInvisibleBinder bndr = split (bndr:acc) ty split acc ty = (reverse acc, ty) ppr_sigma_type _ _ ty = sep [ pprForAll bndrs , pprThetaArrowTy ctxt , pprArrowChain TopPrec (ppr_fun_tail tau) ] where (bndrs, rho) = split1 [] ty (ctxt, tau) = split2 [] rho split1 bndrs (ForAllTy bndr@(Named {}) ty) = split1 (bndr:bndrs) ty split1 bndrs ty = (reverse bndrs, ty) split2 ps (ForAllTy (Anon ty1) ty2) | isPredTy ty1 = split2 (ty1:ps) ty2 split2 ps ty = (reverse ps, ty) -- We don't want to lose synonyms, so we mustn't use splitFunTys here. ppr_fun_tail :: Type -> [SDoc] ppr_fun_tail (ForAllTy (Anon ty1) ty2) | not (isPredTy ty1) = ppr_type FunPrec ty1 : ppr_fun_tail ty2 ppr_fun_tail other_ty = [ppr_type TopPrec other_ty] pprSigmaType :: Type -> SDoc pprSigmaType ty = sdocWithDynFlags $ \dflags -> eliminateRuntimeRep (ppr_sigma_type dflags False) ty pprUserForAll :: [TyBinder] -> SDoc -- Print a user-level forall; see Note [When to print foralls] pprUserForAll bndrs = sdocWithDynFlags $ \dflags -> ppWhen (any bndr_has_kind_var bndrs || gopt Opt_PrintExplicitForalls dflags) $ pprForAll bndrs where bndr_has_kind_var bndr = not (isEmptyVarSet (tyCoVarsOfType (binderType bndr))) pprForAllImplicit :: [TyVar] -> SDoc pprForAllImplicit tvs = pprForAll (zipWith Named tvs (repeat Specified)) -- | Render the "forall ... ." or "forall ... ->" bit of a type. -- Do not pass in anonymous binders! pprForAll :: [TyBinder] -> SDoc pprForAll [] = empty pprForAll bndrs@(Named _ vis : _) = add_separator (forAllLit <+> doc) <+> pprForAll bndrs' where (bndrs', doc) = ppr_tv_bndrs bndrs vis add_separator stuff = case vis of Visible -> stuff <+> arrow _inv -> stuff <> dot pprForAll bndrs = pprPanic "pprForAll: anonymous binder" (ppr bndrs) pprTvBndrs :: [TyVar] -> SDoc pprTvBndrs tvs = sep (map pprTvBndr tvs) -- | Render the ... in @(forall ... .)@ or @(forall ... ->)@. -- Returns both the list of not-yet-rendered binders and the doc. -- No anonymous binders here! ppr_tv_bndrs :: [TyBinder] -> VisibilityFlag -- ^ visibility of the first binder in the list -> ([TyBinder], SDoc) ppr_tv_bndrs all_bndrs@(Named tv vis : bndrs) vis1 | vis `sameVis` vis1 = let (bndrs', doc) = ppr_tv_bndrs bndrs vis1 pp_tv = sdocWithDynFlags $ \dflags -> if Invisible == vis && gopt Opt_PrintExplicitForalls dflags then braces (pprTvBndrNoParens tv) else pprTvBndr tv in (bndrs', pp_tv <+> doc) | otherwise = (all_bndrs, empty) ppr_tv_bndrs [] _ = ([], empty) ppr_tv_bndrs bndrs _ = pprPanic "ppr_tv_bndrs: anonymous binder" (ppr bndrs) pprTvBndr :: TyVar -> SDoc pprTvBndr tv | isLiftedTypeKind kind = ppr_tvar tv | otherwise = parens (ppr_tvar tv <+> dcolon <+> pprKind kind) where kind = tyVarKind tv pprTvBndrNoParens :: TyVar -> SDoc pprTvBndrNoParens tv | isLiftedTypeKind kind = ppr_tvar tv | otherwise = ppr_tvar tv <+> dcolon <+> pprKind kind where kind = tyVarKind tv instance Outputable TyBinder where ppr (Named v Visible) = ppr v ppr (Named v Specified) = char '@' <> ppr v ppr (Named v Invisible) = braces (ppr v) ppr (Anon ty) = text "[anon]" <+> ppr ty instance Outputable VisibilityFlag where ppr Visible = text "[vis]" ppr Specified = text "[spec]" ppr Invisible = text "[invis]" ----------------- instance Outputable Coercion where -- defined here to avoid orphans ppr = pprCo instance Outputable LeftOrRight where ppr CLeft = text "Left" ppr CRight = text "Right" {- Note [When to print foralls] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Mostly we want to print top-level foralls when (and only when) the user specifies -fprint-explicit-foralls. But when kind polymorphism is at work, that suppresses too much information; see Trac #9018. So I'm trying out this rule: print explicit foralls if a) User specifies -fprint-explicit-foralls, or b) Any of the quantified type variables has a kind that mentions a kind variable This catches common situations, such as a type siguature f :: m a which means f :: forall k. forall (m :: k->*) (a :: k). m a We really want to see both the "forall k" and the kind signatures on m and a. The latter comes from pprTvBndr. Note [Infix type variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ With TypeOperators you can say f :: (a ~> b) -> b and the (~>) is considered a type variable. However, the type pretty-printer in this module will just see (a ~> b) as App (App (TyVarTy "~>") (TyVarTy "a")) (TyVarTy "b") So it'll print the type in prefix form. To avoid confusion we must remember to parenthesise the operator, thus (~>) a b -> b See Trac #2766. -} pprDataCons :: TyCon -> SDoc pprDataCons = sepWithVBars . fmap pprDataConWithArgs . tyConDataCons where sepWithVBars [] = empty sepWithVBars docs = sep (punctuate (space <> vbar) docs) pprDataConWithArgs :: DataCon -> SDoc pprDataConWithArgs dc = sep [forAllDoc, thetaDoc, ppr dc <+> argsDoc] where (_univ_tvs, _ex_tvs, eq_spec, theta, arg_tys, _res_ty) = dataConFullSig dc univ_bndrs = dataConUnivTyBinders dc ex_bndrs = dataConExTyBinders dc forAllDoc = pprUserForAll $ (filterEqSpec eq_spec univ_bndrs ++ ex_bndrs) thetaDoc = pprThetaArrowTy theta argsDoc = hsep (fmap pprParendType arg_tys) pprTypeApp :: TyCon -> [Type] -> SDoc pprTypeApp tc tys = pprTyTcApp TopPrec tc tys -- We have to use ppr on the TyCon (not its name) -- so that we get promotion quotes in the right place pprTyTcApp :: TyPrec -> TyCon -> [Type] -> SDoc -- Used for types only; so that we can make a -- special case for type-level lists pprTyTcApp p tc tys | tc `hasKey` ipClassKey , [LitTy (StrTyLit n),ty] <- tys = maybeParen p FunPrec $ char '?' <> ftext n <> text "::" <> ppr_type TopPrec ty | tc `hasKey` consDataConKey , [_kind,ty1,ty2] <- tys = sdocWithDynFlags $ \dflags -> if gopt Opt_PrintExplicitKinds dflags then ppr_deflt else pprTyList p ty1 ty2 | not opt_PprStyle_Debug , tc `hasKey` errorMessageTypeErrorFamKey = text "(TypeError ...)" -- Suppress detail unles you _really_ want to see | tc `hasKey` tYPETyConKey , [TyConApp ptr_rep []] <- tys , ptr_rep `hasKey` ptrRepLiftedDataConKey = unicodeSyntax (char '★') (char '*') | tc `hasKey` tYPETyConKey , [TyConApp ptr_rep []] <- tys , ptr_rep `hasKey` ptrRepUnliftedDataConKey = char '#' | otherwise = ppr_deflt where ppr_deflt = pprTcAppTy p ppr_type tc tys pprTcAppTy :: TyPrec -> (TyPrec -> Type -> SDoc) -> TyCon -> [Type] -> SDoc pprTcAppTy p pp tc tys = getPprStyle $ \style -> pprTcApp style id p pp tc tys pprTcAppCo :: TyPrec -> (TyPrec -> Coercion -> SDoc) -> TyCon -> [Coercion] -> SDoc pprTcAppCo p pp tc cos = getPprStyle $ \style -> pprTcApp style (pFst . coercionKind) p pp tc cos pprTcApp :: PprStyle -> (a -> Type) -> TyPrec -> (TyPrec -> a -> SDoc) -> TyCon -> [a] -> SDoc -- Used for both types and coercions, hence polymorphism pprTcApp _ _ _ pp tc [ty] | tc `hasKey` listTyConKey = pprPromotionQuote tc <> brackets (pp TopPrec ty) | tc `hasKey` parrTyConKey = pprPromotionQuote tc <> paBrackets (pp TopPrec ty) pprTcApp style to_type p pp tc tys | not (debugStyle style) , Just sort <- tyConTuple_maybe tc , let arity = tyConArity tc , arity == length tys , let num_to_drop = case sort of UnboxedTuple -> arity `div` 2 _ -> 0 = pprTupleApp p pp tc sort (drop num_to_drop tys) | not (debugStyle style) , Just dc <- isPromotedDataCon_maybe tc , let dc_tc = dataConTyCon dc , Just tup_sort <- tyConTuple_maybe dc_tc , let arity = tyConArity dc_tc -- E.g. 3 for (,,) k1 k2 k3 t1 t2 t3 ty_args = drop arity tys -- Drop the kind args , ty_args `lengthIs` arity -- Result is saturated = pprPromotionQuote tc <> (tupleParens tup_sort $ pprWithCommas (pp TopPrec) ty_args) | otherwise = sdocWithDynFlags $ \dflags -> pprTcApp_help to_type p pp tc tys dflags style where pprTupleApp :: TyPrec -> (TyPrec -> a -> SDoc) -> TyCon -> TupleSort -> [a] -> SDoc -- Print a saturated tuple pprTupleApp p pp tc sort tys | null tys , ConstraintTuple <- sort = if opt_PprStyle_Debug then text "(%%)" else maybeParen p FunPrec $ text "() :: Constraint" | otherwise = pprPromotionQuote tc <> tupleParens sort (pprWithCommas (pp TopPrec) tys) pprTcApp_help :: (a -> Type) -> TyPrec -> (TyPrec -> a -> SDoc) -> TyCon -> [a] -> DynFlags -> PprStyle -> SDoc -- This one has accss to the DynFlags pprTcApp_help to_type p pp tc tys dflags style | is_equality = print_equality | print_prefix = pprPrefixApp p pp_tc (map (pp TyConPrec) tys_wo_kinds) | [ty1,ty2] <- tys_wo_kinds -- Infix, two arguments; -- we know nothing of precedence though = pprInfixApp p pp pp_tc ty1 ty2 | tc_name `hasKey` starKindTyConKey || tc_name `hasKey` unicodeStarKindTyConKey || tc_name `hasKey` unliftedTypeKindTyConKey = pp_tc -- Do not wrap *, # in parens | otherwise = pprPrefixApp p (parens (pp_tc)) (map (pp TyConPrec) tys_wo_kinds) where tc_name = tyConName tc is_equality = tc `hasKey` eqPrimTyConKey || tc `hasKey` heqTyConKey || tc `hasKey` eqReprPrimTyConKey || tc `hasKey` eqTyConKey -- don't include Coercible here, which should be printed -- normally -- This is all a bit ad-hoc, trying to print out the best representation -- of equalities. If you see a better design, go for it. print_equality = case either_op_msg of Left op -> sep [ parens (pp TyOpPrec ty1 <+> dcolon <+> pp TyOpPrec ki1) , op , parens (pp TyOpPrec ty2 <+> dcolon <+> pp TyOpPrec ki2)] Right msg -> msg where hetero_tc = tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey || tc `hasKey` heqTyConKey print_kinds = gopt Opt_PrintExplicitKinds dflags print_eqs = gopt Opt_PrintEqualityRelations dflags || dumpStyle style || debugStyle style (ki1, ki2, ty1, ty2) | hetero_tc , [k1, k2, t1, t2] <- tys = (k1, k2, t1, t2) | [k, t1, t2] <- tys -- we must have (~) = (k, k, t1, t2) | otherwise = pprPanic "print_equality" pp_tc -- if "Left", print hetero equality; if "Right" just print that msg either_op_msg | print_eqs = Left pp_tc | hetero_tc , print_kinds || not (to_type ki1 `eqType` to_type ki2) = Left $ if tc `hasKey` eqPrimTyConKey then text "~~" else pp_tc | otherwise = Right $ if tc `hasKey` eqReprPrimTyConKey then text "Coercible" <+> (sep [ pp TyConPrec ty1 , pp TyConPrec ty2 ]) else sep [pp TyOpPrec ty1, text "~", pp TyOpPrec ty2] print_prefix = not (isSymOcc (nameOccName tc_name)) tys_wo_kinds = suppressInvisibles to_type dflags tc tys pp_tc = ppr tc ------------------ -- | Given a 'TyCon',and the args to which it is applied, -- suppress the args that are implicit suppressInvisibles :: (a -> Type) -> DynFlags -> TyCon -> [a] -> [a] suppressInvisibles to_type dflags tc xs | gopt Opt_PrintExplicitKinds dflags = xs | otherwise = snd $ partitionInvisibles tc to_type xs ---------------- pprTyList :: TyPrec -> Type -> Type -> SDoc -- Given a type-level list (t1 ': t2), see if we can print -- it in list notation [t1, ...]. pprTyList p ty1 ty2 = case gather ty2 of (arg_tys, Nothing) -> char '\'' <> brackets (fsep (punctuate comma (map (ppr_type TopPrec) (ty1:arg_tys)))) (arg_tys, Just tl) -> maybeParen p FunPrec $ hang (ppr_type FunPrec ty1) 2 (fsep [ colon <+> ppr_type FunPrec ty | ty <- arg_tys ++ [tl]]) where gather :: Type -> ([Type], Maybe Type) -- (gather ty) = (tys, Nothing) means ty is a list [t1, .., tn] -- = (tys, Just tl) means ty is of form t1:t2:...tn:tl gather (TyConApp tc tys) | tc `hasKey` consDataConKey , [_kind, ty1,ty2] <- tys , (args, tl) <- gather ty2 = (ty1:args, tl) | tc `hasKey` nilDataConKey = ([], Nothing) gather ty = ([], Just ty) ---------------- pprInfixApp :: TyPrec -> (TyPrec -> a -> SDoc) -> SDoc -> a -> a -> SDoc pprInfixApp p pp pp_tc ty1 ty2 = maybeParen p TyOpPrec $ sep [pp TyOpPrec ty1, pprInfixVar True pp_tc <+> pp TyOpPrec ty2] pprPrefixApp :: TyPrec -> SDoc -> [SDoc] -> SDoc pprPrefixApp p pp_fun pp_tys | null pp_tys = pp_fun | otherwise = maybeParen p TyConPrec $ hang pp_fun 2 (sep pp_tys) ---------------- pprArrowChain :: TyPrec -> [SDoc] -> SDoc -- pprArrowChain p [a,b,c] generates a -> b -> c pprArrowChain _ [] = empty pprArrowChain p (arg:args) = maybeParen p FunPrec $ sep [arg, sep (map (arrow <+>) args)] {- %************************************************************************ %* * \subsection{TidyType} %* * %************************************************************************ -} -- | This tidies up a type for printing in an error message, or in -- an interface file. -- -- It doesn't change the uniques at all, just the print names. tidyTyCoVarBndrs :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar]) tidyTyCoVarBndrs env tvs = mapAccumL tidyTyCoVarBndr env tvs tidyTyCoVarBndr :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar) tidyTyCoVarBndr tidy_env@(occ_env, subst) tyvar = case tidyOccName occ_env occ1 of (tidy', occ') -> ((tidy', subst'), tyvar') where subst' = extendVarEnv subst tyvar tyvar' tyvar' = setTyVarKind (setTyVarName tyvar name') kind' name' = tidyNameOcc name occ' kind' = tidyKind tidy_env (tyVarKind tyvar) where name = tyVarName tyvar occ = getOccName name -- System Names are for unification variables; -- when we tidy them we give them a trailing "0" (or 1 etc) -- so that they don't take precedence for the un-modified name -- Plus, indicating a unification variable in this way is a -- helpful clue for users occ1 | isSystemName name = if isTyVar tyvar then mkTyVarOcc (occNameString occ ++ "0") else mkVarOcc (occNameString occ ++ "0") | otherwise = occ tidyTyBinder :: TidyEnv -> TyBinder -> (TidyEnv, TyBinder) tidyTyBinder tidy_env (Named tv vis) = (tidy_env', Named tv' vis) where (tidy_env', tv') = tidyTyCoVarBndr tidy_env tv tidyTyBinder tidy_env (Anon ty) = (tidy_env, Anon $ tidyType tidy_env ty) tidyTyBinders :: TidyEnv -> [TyBinder] -> (TidyEnv, [TyBinder]) tidyTyBinders = mapAccumL tidyTyBinder --------------- tidyFreeTyCoVars :: TidyEnv -> TyCoVarSet -> TidyEnv -- ^ Add the free 'TyVar's to the env in tidy form, -- so that we can tidy the type they are free in tidyFreeTyCoVars (full_occ_env, var_env) tyvars = fst (tidyOpenTyCoVars (full_occ_env, var_env) (varSetElemsWellScoped tyvars)) --------------- tidyOpenTyCoVars :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar]) tidyOpenTyCoVars env tyvars = mapAccumL tidyOpenTyCoVar env tyvars --------------- tidyOpenTyCoVar :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar) -- ^ Treat a new 'TyCoVar' as a binder, and give it a fresh tidy name -- using the environment if one has not already been allocated. See -- also 'tidyTyCoVarBndr' tidyOpenTyCoVar env@(_, subst) tyvar = case lookupVarEnv subst tyvar of Just tyvar' -> (env, tyvar') -- Already substituted Nothing -> let env' = tidyFreeTyCoVars env (tyCoVarsOfType (tyVarKind tyvar)) in tidyTyCoVarBndr env' tyvar -- Treat it as a binder --------------- tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar tidyTyVarOcc env@(_, subst) tv = case lookupVarEnv subst tv of Nothing -> updateTyVarKind (tidyType env) tv Just tv' -> tv' --------------- tidyTypes :: TidyEnv -> [Type] -> [Type] tidyTypes env tys = map (tidyType env) tys --------------- tidyType :: TidyEnv -> Type -> Type tidyType _ (LitTy n) = LitTy n tidyType env (TyVarTy tv) = TyVarTy (tidyTyVarOcc env tv) tidyType env (TyConApp tycon tys) = let args = tidyTypes env tys in args `seqList` TyConApp tycon args tidyType env (AppTy fun arg) = (AppTy $! (tidyType env fun)) $! (tidyType env arg) tidyType env (ForAllTy (Anon fun) arg) = (ForAllTy $! (Anon $! (tidyType env fun))) $! (tidyType env arg) tidyType env (ForAllTy (Named tv vis) ty) = (ForAllTy $! ((Named $! tvp) $! vis)) $! (tidyType envp ty) where (envp, tvp) = tidyTyCoVarBndr env tv tidyType env (CastTy ty co) = (CastTy $! tidyType env ty) $! (tidyCo env co) tidyType env (CoercionTy co) = CoercionTy $! (tidyCo env co) --------------- -- | Grabs the free type variables, tidies them -- and then uses 'tidyType' to work over the type itself tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type]) tidyOpenTypes env tys = (env', tidyTypes (trimmed_occ_env, var_env) tys) where (env'@(_, var_env), tvs') = tidyOpenTyCoVars env $ tyCoVarsOfTypesWellScoped tys trimmed_occ_env = initTidyOccEnv (map getOccName tvs') -- The idea here was that we restrict the new TidyEnv to the -- _free_ vars of the types, so that we don't gratuitously rename -- the _bound_ variables of the types. --------------- tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type) tidyOpenType env ty = let (env', [ty']) = tidyOpenTypes env [ty] in (env', ty') --------------- -- | Calls 'tidyType' on a top-level type (i.e. with an empty tidying environment) tidyTopType :: Type -> Type tidyTopType ty = tidyType emptyTidyEnv ty --------------- tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind) tidyOpenKind = tidyOpenType tidyKind :: TidyEnv -> Kind -> Kind tidyKind = tidyType ---------------- tidyCo :: TidyEnv -> Coercion -> Coercion tidyCo env@(_, subst) co = go co where go (Refl r ty) = Refl r (tidyType env ty) go (TyConAppCo r tc cos) = let args = map go cos in args `seqList` TyConAppCo r tc args go (AppCo co1 co2) = (AppCo $! go co1) $! go co2 go (ForAllCo tv h co) = ((ForAllCo $! tvp) $! (go h)) $! (tidyCo envp co) where (envp, tvp) = tidyTyCoVarBndr env tv -- the case above duplicates a bit of work in tidying h and the kind -- of tv. But the alternative is to use coercionKind, which seems worse. go (CoVarCo cv) = case lookupVarEnv subst cv of Nothing -> CoVarCo cv Just cv' -> CoVarCo cv' go (AxiomInstCo con ind cos) = let args = map go cos in args `seqList` AxiomInstCo con ind args go (UnivCo p r t1 t2) = (((UnivCo $! (go_prov p)) $! r) $! tidyType env t1) $! tidyType env t2 go (SymCo co) = SymCo $! go co go (TransCo co1 co2) = (TransCo $! go co1) $! go co2 go (NthCo d co) = NthCo d $! go co go (LRCo lr co) = LRCo lr $! go co go (InstCo co ty) = (InstCo $! go co) $! go ty go (CoherenceCo co1 co2) = (CoherenceCo $! go co1) $! go co2 go (KindCo co) = KindCo $! go co go (SubCo co) = SubCo $! go co go (AxiomRuleCo ax cos) = let cos1 = tidyCos env cos in cos1 `seqList` AxiomRuleCo ax cos1 go_prov UnsafeCoerceProv = UnsafeCoerceProv go_prov (PhantomProv co) = PhantomProv (go co) go_prov (ProofIrrelProv co) = ProofIrrelProv (go co) go_prov p@(PluginProv _) = p go_prov p@(HoleProv _) = p tidyCos :: TidyEnv -> [Coercion] -> [Coercion] tidyCos env = map (tidyCo env)